I'm worried my (male) best friend might be in love with me...how can I be sure without straight out asking?

I've been friends with this guy for roughly 4-5 months. We've gotten really close, and talk about pretty much everything. I'm in a relationship with someone whom I'm engaged to and we've been together almost 6 years. I once cheated on my fiancee and it has haunted me ever since. I'm not concerned about me cheating again but rather becoming more paranoid that my best friend wants to leave his current gf (who incidentally is nothing like him, they don't see eye to eye a lot and have only been going out for 3 or so months) and be with me. He's really a wonderfully nice guy, who most likely has no alterior motives but I'm still really worried. So how can I rid myself of this paranoia without flat out asking him if he wants to sleep with me/have a relationship with me? One of my friends told me that a lot of people just see sex as the next logical step after you've become so close to someone, like in the movie "When Harry Met Sally". Is this always the case with best friends of opposite genders? Help please?? Any advice is greatly appreciated.