Having a girlfriend is a little different from being married, but I still think you need to be aware of respecting his relationship until you know where you stand. From his actions, it's obvious that he thinks you are attractive. Perhaps see if there is a way to spend some time with him. Can you ask him to help you train, for example, or shout him a coffee at the gym cafe? If he isn't interested in a relationship with you, it's likely he will mention his girlfriend to discourage you and then you'll know to back off. To give yourself the best chance, try and make sure that he enjoys being around you. Relax and be yourself. If he is into you, he'll find a way to let you know. For the sake of your own self-esteem, though, make sure he has broken up with his girlfriend before starting a proper relationship with him.