It's her

In this story Asami starts off as an orphan. She meets a small brown girl with the most big beautiful blue eyes, at the orphanage. The blue eyed girl was to young to speak but she would be able to say "avatar". Asami decided to stick with that name and call her "Avatar". They became best friends and promise to each other that they will always stay together. But everything changed once Avatar was adopted. Before Avatar left, she went to hug Asami for the last time and promised her that they would make their way back to each other. Asami stayed with that promised. Soon she was taken in by Katara. But she never let go of that memory, and she knew deep down in her gut that she will find her again. She will find her Avatar.