What does this older man think about me? Should I approach him?

Anonymous

I'd greatly appreciate any opinions/advice!

There is this older (40s) guy around my campus, who I occasionally see/cross paths with. I'll mention that I am in my 20s.

We have never spoken but we've had a few encounters over a long period of time. The first encounter I had with him was in a common area at the college. He sat nearby, and even though I was looking away I kept noticing him gazing at me. He was always facing me. At one point he was talking about something unrelated to another guy, and when I looked up to check the time, I saw him quickly turn to me, smiling. When I left the common area, he looked up into my eyes with his mouth slightly open, until I passed him. I think he may remember me, since he always notices me and will look twice. Whenever he walks past me he stares into my eyes, and when I look back, we hold eye contact until we pass each other. More recently, I was at a school event where clubs/departments host information tables. Upon looking around the room for my friend, I noticed him. I think he noticed me too, because he kept glancing at me even when talking with an older gentleman. Once more, his body was facing me, away from the table he was hosting. He would turn to talk to people, but would always turn back to face me. At one point I noticed him quickly walked by my table, which mind you, was in an inconvenient location. He had utilities near his table, so I was suspicious as to why he went out of his way to take that route. Maybe he was going to try to approach me?

Now, it's probably obvious that I am interested in his behavior. Although I was not the first to stare, I do now. I find him handsome, but I'm not sure what to think of his staring. Also, I think he may be a professor, however, I am graduating soon so I'm not too concerned about that. I just want to see what other people think, since I don't have anyone else to talk to about this. I'd like to get to know him better, so I would appreciate a second opinion! :)

What does this older man think about me? Should I approach him?
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