Can you run cat6a/pvc conduit next to gas hvac exhaust?

I know high efficient units you can (probably.) But this is some older 6" (or more metal piping/flute.)

I want to get some cat6a from my 2nd floor to the basement, and this area seems like a super easy way to make that happen. However I am pretty sure this is a no-no.

I wanted to check with the all powerful reddit before I do anything. But I think drilling down another 2x4 plate between walls is probably the best route forward?

Thank you!