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'