How should I approach a guy at the gym?

So, I’m sure there have probably been people who have asked about situations like this before, but as a woman, I am wondering if it is as “taboo” to approach men in the gym as it is for men to approach women.

There is this guy that I’ve seen in the gym almost every time I’ve been there. I initially noticed him because occasionally, if I see movement out of the corner of my eye, I subconsciously look over for a quick second. I think it is a nervous/anxious thing I do that I sometimes can’t help, but I try to stop when I notice myself doing it. Regardless, there have been a few times when I’ve done that and, incredibly, it always happens to be that guy that I end up making eye contact with. I halfway wonder if he thought it was intentional considering it happened so often early on, but it was completely coincidental and as soon as I realized it was him, I’d always avert my eyes.

Over time of course, I got used to the environment and while I do happen to make eye contact with him occasionally when he crosses my vision, I try to recognize when he’s in my peripherals so I don’t keep darting my eyes over to him accidentally. Despite this, he never seemed bothered and is always very nice and polite to people at the gym. He is pretty attractive too, but I think I more just noticed how kind and helpful he seemed to other people at the gym. I don’t know much about him, but with how approachable he seems to other people, I’ve been considering whether I should approach him at some point in between sets or something just to say hi or try to see if he’d be interested in chatting/getting to know each other.

However, the last thing I want to do is make him uncomfortable. Truly, I’d want to approach him more platonically at first to get to know him, but I’m afraid it may come off as though I am flirting. Which, I mean, I’m not necessarily opposed it, it’s just that I wouldn’t want to make it weird for him since he clearly works out at the gym as often as I do and I wouldn’t want him to feel uncomfortable going to the gym.

So guys, is it okay for a woman to approach you in the gym? And if so, how would you suggest she do it so it’s very low pressure and comfortable?