It's hard...
Reminds me a bit of the situation when I got together with my ex. We were good friends, but I wanted more, and at first he had to tell me he just wanted to be friends. Then about six weeks later, he asked me out.
But when he broke up with me, a few months later, saying "it just doesn't feel right" I wondered if perhaps I'd somehow pushed him into going out with me, which is why it hadn't worked.
All I can say is, DON'T push it, because you could end up losing her as a friend. Or even if she did change her mind, you could end up in the same situation as me - wondering if she ever really cared about you that much in the first place.
Who knows. Perhaps my ex did just have a change of heart and realise he really liked me, back then. And perhaps this girl will, with you. But I wonder...
(Sorry for going on about myself a bit, it was not my original intention)