How to befriend this dude?

So there's this guy that lives in my town who's a year or so older than me. He's super sweet, smart, attractive , (Dark brown hair, icy blue eyes) got a good head on his shoulders, the works.
I don't think he has a gf? Not once in my life have I seen him with another girl in any intimate way.
He always stares at me, and I have no idea why. I'm not drop-dead gorgeous, but I'm not ugly/plainly average either. The problem is that he takes online school now, no idea why, so I hardly ever see him and when I do, he's with a bunch of his friends.
I could be completely misinterpreting his staring and maybe he's just zonin' out, or looking at something behind me. But when he stares and I catch him, he's aware of the direct eye contact and DOES NOT LOOK AWAY so I'm always the one to do it.
We don't text and we've never really talked apart from the occasional "excuse me" or "you can go in front of me" walking up stairs or whatever.
I don't really know what's up with him, but what should I do next time he's looking? I am intersted, I just don't know how to go about it.
Jesus fuck why are guys so confusing
How to befriend this dude?
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