This sounds like the ideal situation to be in.
You are clearly very close. You are friends first, which I happen to think is the most important ingredient to a good, real relationship.
You sound a bit worried that he hasn't broken it off with his girlfriend.
I guess if I were you, I would give him a time frame in my own mind, like 1 month. If he and she are still together in a month, then talk with him about when he said he was breaking up. I think I would not let him know that I was eager to see him romantically, but I would ask as a friend.
If you feel desperate about him, then I would take some time away from him. Desperate feelings only bring out resentment and negative interaction. He wants you as a friend, you value his friendship, if it is destined to turn into something more, it will. Be patient, and enjoy the time you have together. You never know!