This is an interesting question. The Buddha did not teach that there is a Buddha nature, possibly because of this very question.

Later on, in Mahayana Buddhism, the concept of Buddha nature was invented.

What is the fundamental nature of existence? What is Buddha-nature? What is the teaching that cannot be taught?

According to The Buddha, we all are "buddha-nature." We are not separate selves apart from the rest of the world. Buddha-nature is Emptiness. In effect, this means that all individuals, whether human or not, are empty of separate substrata. Although the forms of different individuals are different, their essence is the same. If so, it follows that Buddha-nature is One in every individual. Ultimately, therefore, there is a deep identity between oneself and all other beings. Since nature is all beings, to live in harmony with nature is, ultimately, to live in harmony with oneself.

.

According to The Buddha, we all are "buddha-nature." We are not separate selves apart from the rest of the world. Buddha-nature is Emptiness. In effect, this means that all individuals, whether human or not, are empty of separate substrata. Although the forms of different individuals are different, their essence is the same. If so, it follows that Buddha-nature is One in every individual. Ultimately, therefore, there is a deep identity between oneself and all other beings. Since nature is all beings, to live in harmony with nature is, ultimately, to live in harmony with oneself.

.