I was playing with Tensorflow, needed a new version, and realized that a Tensorflow release without AVX still doesn't exist. Since my prior post on Tensorflow without AVX had been beneficial to a few people, I decided to compile Tensorflow 2.5 for Linux, and put up the wheel here for others' benefit.
Tensorflow 2.5 for Linux without AVX support (155 Megabytes)
and the prior link
Tensorflow 2.3 for Linux without AVX support (126 Megabytes)
Download the file, and then run
$ pip3 install -U <filename.whl>