Welcome. Net::SSLeay isn't installing. If you look at the README it states that the openssl devel should be installed, as per the prerequisites section.

When an automated module installation fails you should read the documentation for the modules which cause the failure. This includes open issues as well as the associated README/INSTALL files.

Try the above, install the devel package using your package manager, then try to install REST::Client. Report back any problems.

Thank you very much! I will try it out and post results back here

I still can’t install the Net::SSLeay. The got past the original error. Here is what I have tried.

 First installed openssl and recompiled

cd /usr/local/src
wget https://www.openssl.org/source/openssl-1.0.2-latest.tar.gz # gett
+ing the openssl package
tar -zxf openssl-1.0.2-latest.tar.gz

# compiled and installed it. 
cd openssl-1.0.2a
 ./config
make
make test
make install

# moved old openssl and created openssl with symbolic link
mv /usr/bin/openssl /root/
ln -s /usr/local/ssl/bin/openssl /usr/bin/openssl
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At this point when I re-ran 'perl MakeFile.PL' and 'make test' for Net::SSLeay. I get the error can't find err.h file, to have it resolved. I created a symbolic like on where look for .h files as following.

 cd /usr/local/include
ln -s /usr/local/ssl/include/openssl

At this point I re-ran 'perl MakeFile.PL' for Net::SSLeay. Now it say

/usr/bin/ld: cannot find -lssl
/usr/bin/ld: cannot find -lcrypto
/usr/bin/ld: cannot find -lz
collect2: error: ld returned 1 exit status

Here is full notes 

# make test
Running Mkbootstrap for SSLeay ()
chmod 644 "SSLeay.bs"
"/usr/bin/perl" "-Iinc" -MExtUtils::Command::MM -e 'cp_nonempty' -- SS
+Leay.bs blib/arch/auto/Net/SSLeay/SSLeay.bs 644
gcc -c   -D_REENTRANT -D_GNU_SOURCE -fno-strict-aliasing -pipe -fstack
+-protector -I/usr/local/include -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BI
+TS=64 -O2 -g -pipe -Wall -Wp,-D_FORTIFY_SOURCE=2 -fexceptions -fstack
+-protector-strong --param=ssp-buffer-size=4 -grecord-gcc-switches -m6
+4 -mtune=generic   -DVERSION=\"1.81\" -DXS_VERSION=\"1.81\" -fPIC "-I
+/usr/lib64/perl5/CORE"   SSLeay.c
SSLeay.xs: In function ‘ssleay_ctx_cert_verify_cb_invoke’:
SSLeay.xs:675:10: warning: variable ‘ssl’ set but not used [-Wunused-b
+ut-set-variable]
     SSL *ssl;
          ^
SSLeay.xs: In function ‘next_proto_select_cb_invoke’:
SSLeay.xs:917:12: warning: unused variable ‘n_a’ [-Wunused-variable]
     STRLEN n_a;
            ^
SSLeay.xs: In function ‘pem_password_cb_invoke’:
SSLeay.xs:1116:12: warning: unused variable ‘n_a’ [-Wunused-variable]
     STRLEN n_a;
            ^
SSLeay.xs: In function ‘tlsext_ticket_key_cb_invoke’:
SSLeay.xs:1288:2: warning: pointer targets in passing argument 2 of ‘P
+erl_newSVpv’ differ in signedness [-Wpointer-sign]
  XPUSHs(sv_2mortal(newSVpv(key_name,16)));
  ^
In file included from /usr/lib64/perl5/CORE/perl.h:5030:0,
                 from SSLeay.xs:141:
/usr/lib64/perl5/CORE/proto.h:2755:19: note: expected ‘const char * co
+nst’ but argument is of type  unsigned char *’
 PERL_CALLCONV SV* Perl_newSVpv(pTHX_ const char *const s, const STRLE
+N len)
                   ^
In file included from /usr/lib64/perl5/CORE/perl.h:3436:0,
                 from SSLeay.xs:141:
/usr/lib64/perl5/CORE/sv.h:1567:5: warning: pointer targets in initial
+ization differ in signedness [-Wpointer-sign]
     ((SvFLAGS(sv) & (SVf_POK)) == SVf_POK \
     ^
/usr/lib64/perl5/CORE/sv.h:1562:22: note: in expansion of macro ‘SvPV_
+flags’
 #define SvPV(sv, lp) SvPV_flags(sv, lp, SV_GMAGIC)
                      ^
SSLeay.xs:1306:29: note: in expansion of macro ‘SvPV’
      unsigned char *pname = SvPV(sname,svlen);
                             ^
/usr/lib64/perl5/CORE/sv.h:1567:5: warning: pointer targets in initial
+ization differ in signedness [-Wpointer-sign]
     ((SvFLAGS(sv) & (SVf_POK)) == SVf_POK \
     ^
/usr/lib64/perl5/CORE/sv.h:1562:22: note: in expansion of macro ‘SvPV_
+flags’
 #define SvPV(sv, lp) SvPV_flags(sv, lp, SV_GMAGIC)
                      ^
SSLeay.xs:1319:28: note: in expansion of macro ‘SvPV’
      unsigned char *pkey = SvPV(skey,svlen);
                            ^
In file included from SSLeay.xs:142:0:
SSLeay.c: In function ‘XS_Net__SSLeay_CLONE’:
/usr/lib64/perl5/CORE/XSUB.h:164:20: warning: unused variable ‘items’ 
+[-Wunused-variable]
 #define dITEMS I32 items = (I32)(SP - MARK)
                    ^
/usr/lib64/perl5/CORE/XSUB.h:172:16: note: in expansion of macro ‘dITE
+MS’
  dSP; dAXMARK; dITEMS
                ^
SSLeay.c:1632:11: note: in expansion of macro ‘dXSARGS’
     dVAR; dXSARGS;
           ^
SSLeay.c: In function ‘XS_Net__SSLeay_read’:
SSLeay.c:2403:7: warning: unused variable ‘RETVAL’ [-Wunused-variable]
  AV * RETVAL;
       ^
SSLeay.c: In function ‘XS_Net__SSLeay_get_shared_ciphers’:
SSLeay.c:3156:6: warning: variable ‘ignored_param2’ set but not used [
+-Wunused-but-set-variable]
  int ignored_param2;
      ^
SSLeay.c:3155:6: warning: variable ‘ignored_param1’ set but not used [
+-Wunused-but-set-variable]
  int ignored_param1;
      ^
In file included from SSLeay.xs:142:0:
SSLeay.c: In function ‘XS_Net__SSLeay_get_session’:
/usr/lib64/perl5/CORE/XSUB.h:183:20: warning: unused variable ‘ix’ [-W
+unused-variable]
 #define dXSI32 I32 ix = XSANY.any_i32
                    ^
SSLeay.c:3476:5: note: in expansion of macro ‘dXSI32’
     dXSI32;
     ^
SSLeay.c: In function ‘XS_Net__SSLeay_FIPS_mode_set’:
SSLeay.c:4410:6: warning: unused variable ‘onoff’ [-Wunused-variable]
  int onoff = (int)SvIV(ST(0))
      ^
In file included from SSLeay.xs:142:0:
SSLeay.c: In function ‘XS_Net__SSLeay_library_init’:
/usr/lib64/perl5/CORE/XSUB.h:183:20: warning: unused variable ‘ix’ [-W
+unused-variable]
 #define dXSI32 I32 ix = XSANY.any_i32
                    ^
SSLeay.c:4441:5: note: in expansion of macro ‘dXSI32’
     dXSI32;
     ^
SSLeay.c: In function ‘XS_Net__SSLeay_P_ASN1_TIME_put2string’:
/usr/lib64/perl5/CORE/XSUB.h:183:20: warning: unused variable ‘ix’ [-W
+unused-variable]
 #define dXSI32 I32 ix = XSANY.any_i32
                    ^
SSLeay.c:7802:5: note: in expansion of macro ‘dXSI32’
     dXSI32;
     ^
SSLeay.xs: In function ‘XS_Net__SSLeay_get_keyblock_size’:
SSLeay.xs:5218:16: warning: unused variable ‘h’ [-Wunused-variable]
  const EVP_MD *h;
                ^
In file included from /usr/lib64/perl5/CORE/perl.h:5071:0,
                 from SSLeay.xs:141:
SSLeay.c: In function ‘XS_Net__SSLeay_OCSP_response_results’:
/usr/lib64/perl5/CORE/embed.h:203:62: warning: ‘revocationTime’ may be
+ used uninitialized in this function [-Wmaybe-uninitialized]
 #define hv_common_key_len(a,b,c,d,e,f) Perl_hv_common_key_len(aTHX_ a
+,b,c,d,e,f)
                                                              ^
SSLeay.xs:6103:28: note: ‘revocationTime’ was declared here
      ASN1_GENERALIZEDTIME *revocationTime, *thisupdate, *nextupdate;
                            ^
rm -f blib/arch/auto/Net/SSLeay/SSLeay.so
LD_RUN_PATH="/usr/lib64" gcc  -shared -O2 -g -pipe -Wall -Wp,-D_FORTIF
+Y_SOURCE=2 -fexceptions -fstack-protector-strong --param=ssp-buffer-s
+ize=4 -grecord-gcc-switches -m64 -mtune=generic -Wl,-z,relro   SSLeay
+.o  -o blib/arch/auto/Net/SSLeay/SSLeay.so  \
   -L/usr -L/usr/lib64 -L/usr/lib -lssl -lcrypto -lz   \

/usr/bin/ld: cannot find -lssl
/usr/bin/ld: cannot find -lcrypto
/usr/bin/ld: cannot find -lz
collect2: error: ld returned 1 exit status
make: *** [blib/arch/auto/Net/SSLeay/SSLeay.so] Error 1
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Excuse the late reply, installing openssl-devel via your package manager (as explained in the module README) will satisfy any required dependencies, then try reinstalling the perl module from cpan.

I am trying to install and REST::Client module on Redhat Linux 8.0

Wow, that's one extremely old operating system. It might save you a whole bunch of headaches in the long run just to replace the O/S with something that's still supported instead. Just a thought.

Sorry must clarify using RHEL 7.2 https://access.redhat.com/articles/3078

Thank you! yes it did complain about headers fles like it can't find err.h file. To have it resolved I created a symbolic like on where look for .h files as following. Though I don't have .h file errors any more I had other issues (as mentioned in one the reply above)

 cd /usr/local/include
ln -s /usr/local/ssl/include/openssl
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