Alright. Our reader is obviously stuck in a dillema: Do I continue with the little sweetness I have with this man and keep my hopes building of a potential future, or confront him and this girl and possibly have the relationship ruined and lose my little 'thing'... but then it becomes clear what the choice is.
YOU NEED TO CONFRONT THIS GUY & THE GIRL.
We, especially when we have something with people, tend to underestimate ourselves and sell ourselves short. But it's the other way around. If he has something with you and there is potential for more, especially in your heart, let him know and let him know the damage he's doing by befriending her. Being straight up, is the key here.
ALSO, If he's willing to say "I'll stop talking to her" "I promise you this, that" then this is obviously more than a best-friend relationship that has more in it and you should work out the kinks before you two become in an 'open relationship' You don't want that. You obviously deserve better, and this is where you need to clarify things.
LETTING him know you want to be "his official girl" or simply if you don't want nothing more(?) is the key to working out this friendship. As for the other girl, you should really let her know how you feel about him and tell her to keep her greasy paws off of him.
Hope I could provide help to you

Thank you!