HOPEFULLY, the girl will would slowly veer away from him, if you two started consistantly dating. If not, and it bothered you, you would wait until she was REALLY into you, and cordially tell her you cant be with someone whos best friends with their ex, because it makes you uncomfortable, and be prepared to walk away. Then, either she'll comply, or you'll just be 'friends' with her also.
Also, find out if she's had any other relationships while being friends with this guy. See if she brings up something like; "He couldnt accept that we were still friends, and he got jealous, and it caused a lot of problems so we didnt work out because of it." If so, you know it'll probably cause problems with you too, if you're uncomfortable with that.