Ok, here's what finally worked for me.

I think the key to success was updating LD_LIBRARY_PATH and PATH to include openssl as I went.

Install and build openssl.

OpenSSL 1.1.1d 10 Sep 2019

cloned openssl repo

Pulled out latest(?) 1.1 branch

git checkout OpenSSL_1_1_1d -b 1_1_1d

./config --prefix=/opt/openssl
make
make install

Add /opt/openssl/lib to your LD_LIBRARY_PATH env var

Add /opt/openssl/bin to your PATH

Install and build python-3.7.6

I installed with --prefix=/opt/python-3.7.6

./configure --prefix=/opt/python-3.7.6  --enable-optimizations --with-openssl=/opt/openssl
make
make install

Add /opt/python-3.7.6/lib to your LD_LIBRARY_PATH env var

Add /opt/python-3.7.6/bin to your PATH

Final Config

LD_LIBRARY_PATH=/opt/openssl/lib:/opt/python-3.7.6/lib:

PATH=/opt/openssl/bin:/opt/python-3.7.6/bin:/opt/idea/latest/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/root/bin

You should have taken the default available python3, that is the python3.6 package in centos7 that would have been easier to setup rather than compile an unsupported version. Suggest you install the supported python3 package in centos

Try doing yum install python36 from repository

sudo yum install -y https://repo.ius.io/ius-release-el7.rpm

Update yum package

 sudo yum update

Install python36 along with pip

sudo yum install -y python36u python36u-libs python36u-devel python36u-pip

Below steps are for python3.7, suggest avoiding unsupported packages. Alternate Steps for pip setup for Centos You need to install pip for python3.7 series Step 1: First install the EPEL Repository

sudo yum install epel-release

Step 2: Installing pip

python37 -m pip

Step 3: Verify if pip was installed properly pip --version

If the command not found error shows up, try

python37 -m ensurepip