No president is universally accepted as having been homosexual, but James Buchanan is the most commonly rumoured to have been so. He never married and had a very close relationship with another man, who was officially his best friend and roommate for around ten years. There is no conclusive evidence as they were never "caught", but a lot of his letters were burned after his death, which does hint at there being something juicy in them. Not that there aren't other reasons for wanting to burn

If nobody smarter than me bothers to reply to this, then you could probably get somewhere just by reading about Buchanan. Just take everything with a grain of salt, since a lot of people have a vested interest in his identity, be it pro-LGBT by showing they've been active in high society for a long time, or slanderous by associating them with one of the least popular presidents in US history. Social norms have also changed quite a bit over the years. The way Sherlock Holmes and John Watson cohabited didn't seem terribly suspicious when the stories were first written, but just take a look at the fandom of the new BBC series... I honestly think the evidence fits just as well to what would today be labeled as an asexual who was either homoromantic, or just preferred the company of guys to that of the ladies.

There was also discussion about him previously on this subreddit that you might want to check out.