How do I go about this?

There is this guy at the gym I go to who peaks my interest but there is just one problem and it's that I'm not even sure he is gay. He has shown possible signs of it such as I caught him looking at me through the mirror while I was stretching for squats and when he realized I noticed him he looked away really quick (he didn't notice one time and he was staring for a good 5-7 seconds) or every time we make eye contact we always give each other a smile.I just want to know that if I do strike up a conversation with him, how would I find out what he's into? Do I just ask him straight up or do I go more along the line of "Sorry if I got the wrong idea but do you want to get drinks sometime?"