Theoretically possible, but highly unlikely. According to Avatar canon, the new avatar is born into the next element / nation in the cycle (fire->air->water->earth).
So for the avatar to father himself, he would have to get together with a female bender of the next element in the cycle, impregnate her and then die before the 5th month of the pregnancy (most philosophies that belive in reincarnation of discrete souls/persons believe that the soul indwels the foetus around the middle of the pregnancy/second trimester).
Once upon a time it was also stated that the avatar is born every 100 years, but since it was later revealed that several avatars lived much longer than that (e.g. Kyoshi lived 230 years or so) that was probably just a crossed wire somewhere.