You might have someone that consideres you their best friend but has not vocalized it yet. For example I have had people tell me I am their best friend but I really haven't felt that someone is my best friend yet, that is because I have seen people who do not even call me their best friend treat me better in some aspects. So the fact that someone calls you their best friend doesn't mean they will treat you much better than someone who doesn't.
To become someone's best friend, I find that being there for them in their highs and lows help. Some people want to be around others only when everything is fine. When things are bad they leave that person to their luck. Hence such person can't be considered a best friend even if they did not do that intentionally. Another thing is showing genuine care.
One thing you can do is ask your close friends, who is their best friend and why. You might be surprised that one day someone might mention you and you never knew. If you do not have any close friend then start by being friendly to people you like, that way you might start building a friendship.
I hope these suggestions help. As usual do what feels best for you. It might take a while to get a best friend, but when you do, you will feel it was worth the wait.
