A solid friendship isn't something that can be forced, and unless two people are interested in each other and care about being friends, I don't think it's something that can really work out. That may or may not be your situation, but in any case, knowing why it's so important for you to become friends with this girl would make it easier to understand why you just can't seem to do it.

Do you want to be friends with this new person just because she seems to be becoming close with your best friend? Are you feeling left out when they get together? That would certainly be understandable. Maybe ask yourself whether you would want to be friends with this girl if she weren't close with your best friend.

Close friendships are based on shared interests and personalities. So if you really want to become friends with this girl because you like her and know that you have some sort of bond, then you should reach out to her. Making friends isn't always easy, but perhaps you can focus on what you like about her and propose doing something together that would interest you both.