Eu corro um script que é assim:
version=(version to install)
yum install gcc dstat -y
cd /usr/local/src
wget https://www.openssl.org/source/$version.tar.gz
tar -zxf $version.tar.gz
cd $version
./config -Wl,--enable-new-dtags,-zlib,-nossl3,-rpath,'$(LIBRPATH)'
make
make install
mv /usr/bin/openssl /root #Or substitute where you'd like to back up the old one
ln -sf /usr/local/bin/openssl /usr/bin/openssl
#Adjusting this to whatever you get from the output of "which openssl."