Is it acceptable to approach my gym crush at the gym? (I’m a women)

There’s this guy at the gym who I had a very small interaction with once. I immediately got nervous during that interaction because I noticed just how attractive he actually was. We were both very smiley and body language was giving from the both of us. From that moment on I noticed we kept locking eyes and looking at each other for the rest of the workout. When I walked out the gym, I sat in my car for a minute and noticed he walked out the gym too and his eyes were searching the parking lot till he seen me in my car. He got in his car and left though. Fast forward to yesterday, he was at the gym again (we both got there at the same time) and we were locking eyes again multiple times. I finished my workout and got in my car, he walked out the gym immediately after I did and got in his car and left. I’m feeling like he’s definitely into me but afraid to bother or approach me. When I’m working out, he seems to move around the gym to be near me. I don’t know if he’s waiting for me to make a move or what??? I’m definitely into him but just wish he would approach me. Does this mean I’m just going to have to or should I stand my ground and hope he will?