Thanks for your quick response. MinGw is already installed on host. It gets automatically installed once we open the CPAN for the first time in command prompt. But I installed it again and it got failed on last step:

C:\>ppm install MinGW
Downloading ActiveState Package Repository packlist...done
Updating ActiveState Package Repository database...done
Downloading Ilyaz packlist...done
Downloading test packlist...done
Syncing perl PPM database with .packlists...done
Syncing site PPM database with .packlists...done
ppm install failed: Can't find any package that provides MinGW
C:\>
[download]

I tried again with "perl Makefile.PL machine=none" and got below response now:

C:\Perl64\cpan\sources\authors\id\I\IL\ILYAZ\modules\Math-Pari-2.01080
+605>perl Makefile.PL machine=none
Set up gcc environment - gcc.exe (rubenvb-4.5.4) 4.5.4
Setting up Math::Pari with Perl 5.016001 on MSWin32 version 5.2;
   cc=C:\Perl64\site\bin\gcc.exe, gccversion=gcc.exe (rubenvb-4.5.4) 4
+.5.4, cccdlflags=' ',
   ccflags='-DNDEBUG -DWIN32 -D_CONSOLE -DNO_STRICT -DWIN64 -DCONSERVA
+TIVE -DPERL_TEXTMODE_SCRIPTS -DUSE_SITECUSTOMIZE -
DPERL_IMPLICIT_CONTEXT -DPERL_IMPLICIT_SYS -DUSE_PERLIO -DHASATTRIBUTE
+ -fno-strict-aliasing -mms-bitfields',
   optimize='-O2',
   ld=C:\Perl64\site\bin\g++.exe, ldflags='-L"C:\Perl64\lib\CORE"'.
Found GP/PARI build directory in ./pari-2.1.7
     (integer-formatted version 2001007).

  ### GP/PARI library version 2.1.* has many problems fixed in version
+s 2.3.*.

  ### Especially important are the problems with symbols `hiremainder'
+ and
  ### `overflow' - if your build fails and error messages contain thes
+e
  ### words, updating to 2.3.* might allow your use of fast processor-
+specific
  ### assembler code.)

  ### Switching to 2.3.* should be as simple as giving Makefile.PL an 
+option
  ###           version23_ok=1
  ###   (if you or Makefile.PL already downloaded-and-extracted versio
+n-2.1.*
  ###    distribution, give an extra option, force_download).
  ### Alternatively, give option
  ###           paridir=DIRECTORY-of-extracted-distribution

  ### However, keep in mind: v.2.3.* supports only plotting to PostScr
+ipt.

...Will not overwrite libPARI/paricfg.h...  (remove it manually if nee
+ded)
   You may also want to remove libPARI/paricfg.h if your configuration
+ changed
   from the time of the first build in this directory...
Note (probably harmless): No library found for -lm
Note (probably harmless): No library found for -lkernel32
Note (probably harmless): No library found for -luser32
Note (probably harmless): No library found for -lgdi32
Note (probably harmless): No library found for -lwinspool
Note (probably harmless): No library found for -lcomdlg32
Note (probably harmless): No library found for -ladvapi32
Note (probably harmless): No library found for -lshell32
Note (probably harmless): No library found for -lole32
Note (probably harmless): No library found for -loleaut32
Note (probably harmless): No library found for -lnetapi32
Note (probably harmless): No library found for -luuid
Note (probably harmless): No library found for -lws2_32
Note (probably harmless): No library found for -lmpr
Note (probably harmless): No library found for -lwinmm
Note (probably harmless): No library found for -lversion
Note (probably harmless): No library found for -lodbc32
Note (probably harmless): No library found for -lodbccp32
Note (probably harmless): No library found for -lcomctl32
Note (probably harmless): No library found for -lmsvcrt
...Via command-line: processor family `none'
...I will  use portable assembler-less build
...Assembler is not GNU assembler
Note (probably harmless): No library found for -lm
Note (probably harmless): No library found for -lkernel32
Note (probably harmless): No library found for -luser32
Note (probably harmless): No library found for -lgdi32
Note (probably harmless): No library found for -lwinspool
Note (probably harmless): No library found for -lcomdlg32
Note (probably harmless): No library found for -ladvapi32
Note (probably harmless): No library found for -lshell32
Note (probably harmless): No library found for -lole32
Note (probably harmless): No library found for -loleaut32
Note (probably harmless): No library found for -lnetapi32
Note (probably harmless): No library found for -luuid
Note (probably harmless): No library found for -lws2_32
Note (probably harmless): No library found for -lmpr
Note (probably harmless): No library found for -lwinmm
Note (probably harmless): No library found for -lversion
Note (probably harmless): No library found for -lodbc32
Note (probably harmless): No library found for -lodbccp32
Note (probably harmless): No library found for -lcomctl32
Note (probably harmless): No library found for -lmsvcrt
Writing Makefile for Math::PARI::libPARI
Writing MYMETA.yml and MYMETA.json
Writing Makefile for Math::Pari
Writing MYMETA.yml and MYMETA.json

C:\Perl64\cpan\sources\authors\id\I\IL\ILYAZ\modules\Math-Pari-2.01080
+605>
[download]

C:\Perl64\cpan\sources\authors\id\I\IL\ILYAZ\modules\Math-Pari-2.01080
+605>dmake install
cd libPARI && C:\Perl64\site\bin\dmake.exe
C:\Perl64\site\bin\gcc.exe -c  -I .././pari-2.1.7/src -I .././pari-2.1
+.7/src/headers -I .././pari-2.1.7/src/graph -I .
-DNDEBUG -DWIN32 -D_CONSOLE -DNO_STRICT -DWIN64 -DCONSERVATIVE -DPERL_
+TEXTMODE_SCRIPTS -DUSE_SITECUSTOMIZE -DPERL_IMPLIC
IT_CONTEXT -DPERL_IMPLICIT_SYS -DUSE_PERLIO -DHASATTRIBUTE -fno-strict
+-aliasing -mms-bitfields -DPERLDLL -O2      -DVERS
ION=\"\"        -DXS_VERSION=\"\"  -Derr=pari_err -DASMINLINE -DGCC_IN
+LINE -DDYNAMIC_PLOTTING -o highlvl.o .././pari-2.1
.7/src/gp/highlvl.c
In file included from .././pari-2.1.7/src/headers/pari.h:94:0,
                 from .././pari-2.1.7/src/gp/highlvl.c:21:
./pariinl.h: In function 'new_chunk':
./pariinl.h:368:18: warning: cast to pointer from integer of different
+ size
./pariinl.h:369:26: warning: cast to pointer from integer of different
+ size
./pariinl.h:369:36: warning: cast to pointer from integer of different
+ size
./pariinl.h:376:10: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpcopy':
./pariinl.h:411:22: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'stosmall':
./pariinl.h:501:10: warning: cast to pointer from integer of different
+ size
./pariinl.h: In function 'affii':
./pariinl.h:512:22: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'affsi':
./pariinl.h:520:7: warning: cast from pointer to integer of different 
+size
./pariinl.h: In function 'affsr':
./pariinl.h:532:10: warning: cast from pointer to integer of different
+ size
./pariinl.h:538:28: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpaff':
./pariinl.h:544:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:545:10: warning: cast from pointer to integer of different
+ size
./pariinl.h:547:10: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'cmpir':
./pariinl.h:567:20: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'addssz':
./pariinl.h:585:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:589:24: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'subrr':
./pariinl.h:612:29: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mulssz':
./pariinl.h:660:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:664:24: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'divisz':
./pariinl.h:794:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:798:24: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'divsiz':
./pariinl.h:809:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:812:19: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'divssz':
./pariinl.h:826:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:829:24: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpcmp':
./pariinl.h:861:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:862:13: warning: cast from pointer to integer of different
+ size
./pariinl.h:863:11: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpadd':
./pariinl.h:869:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:870:13: warning: cast from pointer to integer of different
+ size
./pariinl.h:871:11: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpsub':
./pariinl.h:877:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:878:13: warning: cast from pointer to integer of different
+ size
./pariinl.h:879:11: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpmul':
./pariinl.h:885:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:886:13: warning: cast from pointer to integer of different
+ size
./pariinl.h:887:11: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'mpdiv':
./pariinl.h:893:7: warning: cast from pointer to integer of different 
+size
./pariinl.h:894:13: warning: cast from pointer to integer of different
+ size
./pariinl.h:895:11: warning: cast from pointer to integer of different
+ size
./pariinl.h: In function 'gtodouble':
./pariinl.h:917:7: warning: cast from pointer to integer of different 
+size
In file included from c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86
+_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw
32/include/winnt.h:1446:0,
                 from c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86
+_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw
32/include/windef.h:137,
                 from c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86
+_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw
32/include/windows.h:59,
                 from .././pari-2.1.7/src/gp/highlvl.c:77:
c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86_64-w64-mingw32/4.5.4/
+../../../../x86_64-w64-mingw32/include/intrin.h: A
t top level:
c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86_64-w64-mingw32/4.5.4/
+../../../../x86_64-w64-mingw32/include/intrin.h:30
6:5: error: conflicting types for 'abs'
In file included from c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86
+_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw
32/include/windows.h:62:0,
                 from .././pari-2.1.7/src/gp/highlvl.c:77:
c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86_64-w64-mingw32/4.5.4/
+../../../../x86_64-w64-mingw32/include/winuser.h:4
070:72: error: expected ';', ',' or ')' before 'gpsi'
c:\perl64\site\lib\auto\mingw\bin\../lib/gcc/x86_64-w64-mingw32/4.5.4/
+../../../../x86_64-w64-mingw32/include/winuser.h:4
071:75: error: expected ';', ',' or ')' before 'gpsi'
.././pari-2.1.7/src/gp/highlvl.c: In function 'type0':
.././pari-2.1.7/src/gp/highlvl.c:201:25: warning: cast from pointer to
+ integer of different size
.././pari-2.1.7/src/gp/highlvl.c:204:8: warning: cast from pointer to 
+integer of different size
.././pari-2.1.7/src/gp/highlvl.c:218:12: warning: cast from pointer to
+ integer of different size
dmake.exe:  Error code 129, while making 'highlvl.o'
dmake.exe:  Error code 255, while making 'libPARI\libPARI.a'

C:\Perl64\cpan\sources\authors\id\I\IL\ILYAZ\modules\Math-Pari-2.01080
+605>
[download]

We can observe the errors in last two lines:

MinGw is already installed on host ... Any idea how to overcome this?

Your version of MinGW/gcc is very old, and since the problem is with mingw64 headers, first thing I would try is install a newer MinGW/gcc -- whatever the mingw64 equivalent is of

mingw-get upgrade gcc-core-bin
[download]

I feel your pain unfortunately this module is useless to many people the guy who wrote this needs to remove it or make it clear, the instructions on failure are useless to me and im getting the same as you did you manage to resolve this issue?