The painting is known as Salvator Mundi (Saviour of the World).
It is thought that it will be the highest auction price for a work by an Old Master - the artists who painted in Europe before the 19th Century.
Leonardo da Vinci died in 1519 and there are fewer than 20 of his paintings in existence.
Just one is thought to be in private hands - the Salvator Mundi, believed to have been painted sometime after 1505.
It shows Christ with one hand raised, the other holding a glass sphere.
In 1958 it was sold at auction in London for $60. By then the painting was generally reckoned to be the work of a follower of Leonardo and not the work of Leonardo himself.