They claim that they can remember the painting hanging in the family house: it originally belonged to their father, who was shot by the Nazis in 1937.
His children moved to England, but their mother stayed in Germany until 1940, when she escaped to Belgium with the family's art collection.
During the war she was forced to sell off the collection at derisory prices to survive.
Since the Tate acquired the painting - Jan Griffier's View of Hampton Court Palace - in 1961, it has been on almost continuous display. It has been valued at pounds 120,000-200,000.
Last April, 23 museums and galleries began research to identify paintings and objets d'art stolen by the Nazis or forcibly sold.
Nicholas Serota, the director of the Tate Gallery, said yesterday that an investigation had been launched.
The Holocaust Educational Trust said the family went to Sotheby's with photographs of their entire collection and asked the auctioneers if they recognised any of them. It was then discovered that the painting was in the Tate.
In June the Foundation for Prussian Cultural Heritage agreed to return a pounds 3m Van Gogh painting to Gerta Silberberg, who lives in the Midlands. The Nazis had forced her father to sell, and it had ended up in the National Gallery in Berlin.
The Seattle Art Museum has also agreed to return a Matisse to the heirs of a French Jewish art dealer.
t The Government is to make the first interim payments to Holocaust victims whose assets were seized by British authorities during the war, according to a report in the Jewish Chronicle. It announced in March that it would be looking at claims for compensation.