Pay attention: you cannot install arbitrary versions of tensorflow, they have to correspond to your python installation, which isn’t conveyed by most of the answers here. This is also true for the current wheels like here (from this answer above). For this example, the cp35-cp35m found inside the url hints that it is for Python 3.5.x

A huge list of different wheels/compatibilities can be found here on github.
By using this, you can downgrade to almost every availale version in combination with the respective for python. For example:

pip install tensorflow==2.0.0

^{(note that previous to installing Python 3.7.8 alongside version 3.8.3 in my case, you would get this:}

ERROR: Could not find a version that satisfies the requirement tensorflow==2.0.0 (from versions: 2.2.0rc1, 2.2.0rc2, 2.2.0rc3, 2.2.0rc4, 2.2.0, 2.3.0rc0, 2.3.0rc1)
ERROR: No matching distribution found for tensorflow==2.0.0

^{this also holds true for other non-compatible combinations.)}

This should also be useful for legacy CPU without AVX support or GPUs with a compute capability that’s too low.

If you only need the most recent releases (which it doesn’t sound like in your question) a list of urls for the current wheel packages is available on this tensorflow page. That’s from this SO-answer.

^{Note: This link to a list of different versions didn’t work for me.}