The future Nazi dictator was rejected twice by the Academy of Fine Arts, Vienna, which cited “unfitness for painting” and suggested he try architecture.
Richard Westwood-Brookes from Mullock's Specialist Auctioneers, which is selling the painting, told the Daily Telegraph that the two may have known each other in Vienna, and that Freud may have bought the painting from Hitler.
He said: “We will never know for certain whether this was Freud's, but it raises the tantalising prospect that the two men might have met.”
The painting will be sold in Lulow, Shropshire on March 2.