What does it mean when guys look at you all the time but never approach you?

You already understand something important here: that you are inviting these men to approach you by locking eyes with them and smiling. This is how the first moment of contact in dating usually works among emotionally mature straight adults: the woman invites, the man approaches. What you're coming up against here is that in the gym there's another norm of behavior operating in the background: men should respect the personal space of attractive women. These men are noticing your invitation, but it's not strong enough to overcome that other norm.

You know they want to approach you, but you don't want to make the move yourself because that would lead to certain dating dynamics you're trying to avoid. So what you need to do is find a stronger way to invite them to approach you without crossing the line into making a move yourself. Actually it's pretty simple: you just need to break the silence with a totally non-committal statement about a neutral topic, like the weather, the music, the number of other people there that day, etc. If a conversation doesn't immediately follow that's still OK because you've broken the silence, so he knows he can approach you later on if he wants to.

/r/AskMen Thread