Guys, I recently noticed that this guy at the gym is staring at me. We sometimes catch each other's eyes. But he never try to approach me though?

It's been a month maybe and whenever I go to gym, I find myself looking for him. Then when he's there, sometimes he'd try to workout/exercise beside me, but not always though. And we sometimes have eye-to-eye contact for like 2-3 seconds. I get uncomfortable and shy, so I stare away. But he never try to approach or even smile at me. Why? Is it because he knows I like him so he enjoys the attention he is getting from me? Is that it?

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It's been a month maybe and whenever I go to gym, I find myself looking for him. Then when he's there, sometimes he'd try to workout/exercise beside me, but not always though. And we sometimes have eye-to-eye contact for like 2-3 seconds. I get uncomfortable and shy, so I stare away. He has approached me twice before, to ask if we could use the same machine alternately. I agreed. But after that, nothing. Just staring? He didn't approach me again after that but I see him looking at me sometimes.
Guys, I recently noticed that this guy at the gym is staring at me. We sometimes catch each other's eyes. But he never try to approach me though?
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