Do guys like when you approach them? Help a shy girl out?

Question

Do guys like when you approach them? Help a shy girl out?

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I like a guy that comes to the gym I work at, and every since I did his membership I've wanted to get to know him. The problem is that I am really shy and whenever I see him I get very nervous and can't focus (it makes it seem like I don't like him). I suspect that he likes me back because I have overheard guys in the weightroom saying that this boy in particular does like me (of course he is not around when they talk about it). I know he was interested in another girl but people are claiming the girl was just trying to use him because apparently he has money. I do not want his money nor am I interested in a 'Netflix & Chill' situation, I really want to get to know him and possibly start a relationship with him (if he's interested of course!). I want my approach to be sincere and not awkward lol, how should a shy girl go about approaching this guy?

I also don't want to make things weird since I will be approaching him at my job and I don't want to scare him away! :/