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Cupid Complaining to Venus, by Lucas Cranach the Elder, the German artist, was bought by the gallery in 1963 and is worth millions of pounds today.
If claimants to the work, such as descendants of the original owners, come forward, it will go into an official process to determine if they are entitled to have the painting returned or to receive a payout.
The National made its admission after it was told that the painting had been taken from a warehouse in southern Germany in 1945 by Patricia Lochridge Hartwell, an American reporter. The information came to light when Hartwell’s son Jay contacted the gallery.
The painting was almost certainly stolen by the Nazis from Jews and may have been one of thousands of works looted by Hermann Goering, Hitler’s deputy.
“We are acknowledging that there might be a claim on this painting,” said Charles Saumarez Smith, director of the National. “We simply felt under an obligation to make it public that there is a question mark.”
So far six works in British galleries — including the Tate and the British Museum — have been identified as Nazi loot and resulted in payouts. The Cranach would be by far the most valuable, although the claimants would not receive its full market value under restitution rules.
Cupid Complaining to Venus, which depicts the young god telling the goddess that he has been stung by some bees, was painted in about 1525 by Cranach, a friend of Martin Luther, the theologian who inspired the Reformation.
Although it is not certain that the work was owned by a Jewish family, there are no official records of its whereabouts from 1909 to 1945.
After the Nazis came to power in Germany in 1933 they began stealing the possessions of Jews. The process accelerated in the war, when museums across German-occupied Europe were also plundered.
Goering was the most avid looter and appointed agents throughout Europe to scour homes and galleries for plum items to add to his collection, including paintings, sculptures, Roman artefacts, jewellery and tapestries.
If the Cranach, one of nine by the artist owned by the National, had been taken from a museum rather than a private individual, it would have been catalogued and is likely to have been returned after the war.
According to the next issue of The Art Newspaper, Hartwell was reporting in southern Germany at the end of the war.
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