My Trek 520 currently has 700 x 35 tires (stock - they lasted over 5000 miles).
I’m looking for replacements and am wondering if any 700 x tires will fit.
I’m specifically looking at 700 x 32s which I’m guessing will work but want confirmation.
It depends on how wide the rims are. Sheldon Brown’s tire sizing page has a table of what width tires are safe to use, as a function of rim width. (That’s the interior rim width.) This is a very conservative table though; I’ve seen bikes with tires that are too wide, according to this table.
I’m sure 700x32 is fine, but I’d hesitate to recommend anything narrower without knowing your exact rim width. Especially since some “700x28” tires are narrower than others.