Steps as I followed

Install the Openssl in a local directory. 

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


Make and install Openssl

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

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 resloved 
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. Not 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

I went ahead and installed openssl-devel package 'yum install openssl-devel' 



##</code><code>##

 SULLR/IO-Socket-SSL-2.049.tar.gz
one dependency not OK (Net::SSLeay); additionally test harness failed
  /usr/bin/make test -- NOT OK
//hint// to see the cpan-testers results for installing this module, try:
  reports SULLR/IO-Socket-SSL-2.049.tar.gz
  OALDERS/LWP-Protocol-https-6.07.tar.gz
  Has already been unwrapped into directory /root/.cpan/build/LWP-Protocol-https-6.07-0
  OALDERS/LWP-Protocol-https-6.07.tar.gz
  Has already been prepared
Running make for O/OA/OALDERS/LWP-Protocol-https-6.07.tar.gz
Warning: Prerequisite 'IO::Socket::SSL => 1.54' for 'OALDERS/LWP-Protocol-https-6.07.tar.gz' failed     when processing 'SULLR/IO-Socket-SSL-2.049.tar.gz' with 'make_test => NO one dependency not OK (Net:    :SSLeay); additionally test harness failed'. Continuing, but chances to succeed are limited.
cp lib/LWP/Protocol/https.pm blib/lib/LWP/Protocol/https.pm
Manifying 1 pod document
  OALDERS/LWP-Protocol-https-6.07.tar.gz
  /usr/bin/make -- OK
Running make test
PERL_DL_NONLAZY=1 "/usr/bin/perl" "-MExtUtils::Command::MM" "-MTest::Harness" "-e" "undef *Test::Har    ness::Switches; test_harness(0, 'blib/lib', 'blib/arch')" t/*.t
t/apache.t ....... ok
t/https_proxy.t .. skipped: no recent version of IO::Socket::SSL::Utils
All tests successful.
Files=2, Tests=5,  2 wallclock secs ( 0.05 usr  0.01 sys +  0.58 cusr  0.06 csys =  0.70 CPU)
Result: PASS
  OALDERS/LWP-Protocol-https-6.07.tar.gz
Tests succeeded but one dependency not OK (IO::Socket::SSL)
  OALDERS/LWP-Protocol-https-6.07.tar.gz
  [dependencies] -- NA
  KKANE/REST-Client-273.tar.gz
  Has already been unwrapped into directory /root/.cpan/build/REST-Client-273-0
  KKANE/REST-Client-273.tar.gz
  Has already been prepared
Running make for K/KK/KKANE/REST-Client-273.tar.gz
Warning: Prerequisite 'LWP::Protocol::https => 0' for 'KKANE/REST-Client-273.tar.gz' failed when pro    cessing 'OALDERS/LWP-Protocol-https-6.07.tar.gz' with 'make_test => NO one dependency not OK (IO::So    cket::SSL)'. Continuing, but chances to succeed are limited.

KKANE/REST-Client-273.tar.gz
Tests succeeded but one dependency not OK (LWP::Protocol::https)
  KKANE/REST-Client-273.tar.gz
  [dependencies] -- NA
Failed during this command:
 MIKEM/Net-SSLeay-1.81.tar.gz                 : make NO
 SULLR/IO-Socket-SSL-2.049.tar.gz             : make_test NO one dependency not OK (Net::SSLeay); ad    ditionally test harness failed
 OALDERS/LWP-Protocol-https-6.07.tar.gz       : make_test NO one dependency not OK (IO::Socket::SSL)
 KKANE/REST-Client-273.tar.gz                 : make_test NO one dependency not OK (LWP::Protocol::h    ttps)