How about this - instead of trying to change the guy, accept him as he is - a person who doesn't talk much. The nice thing about this is that he might be a really great listener. Why not, instead of trying to get him to talk, you talk about yourself and what interest you and open up to him - most chances are is that to some degree, he'll follow through. If not, they you found a perfect partner to talk to.
A lot of time women and men have different definition of what closeness is and try to change the other to match their expectation. Maybe you can find other ways to feel close - do something fun together, listen to music, do something together that require no talking but action (how about mountain climbing? flying a kite? going to a lecture or a concert?).