
I been going to the gym and normally I just get scanned in by the person in the gym. I never noticed the guy that scanned me in. It's probably been like one or two months now that I notice he has been giving me strong eye contact when I catch his eyes on me he keeps them locked but doesn’t smile at me he just keeps staring and I assume he stops staring once I walk directly pass him.
On his off days he works out and his eyes gazes upon me and I caught that about twice now. When his eyes meets mines I just try to ignore his stare and look away or pretend to drink from my water bottle as I walk pass him just to avoid the eye contact. I really had no interest in him till I have been noticing him staring at me and not letting his eyes drift off to something off when his eyes meets mines.
My interest now is to try to figure out if he likes me or not. What is so funny is that I ran into him at the store yesterday or he ran into me. I was shopping
around and he walked past me and I knew he did not need anything in my aisle cause he just walk past And it's a small store so maybe he saw me in that aisle and just wanted to walk past me and when he knew i saw him he said oh hey! We talked for a brief second and he told me how I always work on cardio either bike or in the pool for really long and he said he is going to work out tonight and I said ok I might see you there then. As he left he later said “hey maybe you can buy me something and give it to me then” I just laughed and said sure. I was shocked to see him at the store. I really honestly had no interest in him (basically I didn’t even knew he existed) till I notice he has been locking his eye on me when I walk past him. I didn’t even end up going to the gym I am trying to avoid him now cause I do not know what to say to him when I see him again btw I am extremely shy that is why I been avoiding his eye contact with me

and don't worry about it, he's not worth stressing out over. 
Unless of course he gives you creepy vibes in any way, then just keep it strictly business and hopefully he'll take a hint. And if you're unsure whether or not you like him, well, talking to him and getting to know him will definitely help you figure that out.