Yes, I am 100% sure a man and woman can be best friends. You for example could be her best guy friend, though it doesn't necessarily mean she sees you as a potential boyfriend. It just simply means she enjoys her friendship with you, and probably wants to remain just friends. If that is the case, you need to be respectful of that. If she sees you in a different light though, it is quite possible your friendship with her could catch fire (aka transition from friendship to romance). Just be yourself without making your expectations too high, and who knows, the friendship might blossom into something else when you least expect it.
Also, even if the woman (or even you for that matter) is in a relationship with someone else, you can still have the woman be one of your best friends even if she or you were seeing someone else, just as long as the other person approves of the friendship.