The painting has an estimated worth of €13.9 to €19.3 million ($18 to 25 million), according to Christie's and Sotheby's auction houses.
A number of Klimt paintings, including Portrait of Gertrud Loew, were collected by Gustav Ucicky, a Nazi propaganda filmmaker who was an illegitimate son of Klimt, and are now held by his elderly widow Ursula, who set up the Klimt Foundation.
Gertrude Loew was the daughter of an intellectual Vienna physician who was a friend of Klimt. The portrait is considered to be one of the finest examples of the series of paintings now known as "Klimt's Women".
It was claimed by her son, Dr Anthony Felsovanyi. Felsovanyi said that when Adolf Hitler marched into Vienna in 1938, his family fled, and his mother left some of their possessions with friends for safekeeping. One friend apparently gave the Klimt portrait to her boyfriend in the Gestapo.
Legal experts have now said that they believe this story is true and that there should be a “fair and equitable solution”.
“In 1938 the painting was hanging in Ms Felsövanyi’s home, in 1942 it was in the possession of Gustav Ucicky. Meanwhile the Felsövanyi family had fled Austria. It’s not important whether Ucicky acted badly - the painting passed through many hands before it came to him,” said the former Administrative Court President Clemens Jabloner.
The Klimt Foundation’s lawyer, Andreas Nödl, will now work with the legal representative of the Felsövanyi heirs to reach an amicable solution.
The Klimt Foundation also holds five drawings of disputed provenance, which will also be restituted.
The Portrait of Gertrud Loew and the drawings are due to be shown in an exhibition at Vienna’s MAK museum in mid December, called "Ways of modernity, Josef Hoffmann, Adolf Loos and the consequences". Information about their history will be included in the exhibition notes.
The non-profit Klimt Foundation was set up last year by Ursula Ucicky, to preserve and research the life and work of the painter.
Since pressure to return art stolen by the Nazis began in the 1990s, Austrian museums have returned a dozen stolen Klimt masterpieces.
In 2001 Austria passed a law based on the Washington Agreement, creating the General Settlement Fund for Victims of National Socialism.
Its object was to develop solutions to resolve as yet unresolved settlement issues. It allows compensation claims for loss of business assets, real estate, capital assets, movable property, occupational and educational losses and other losses or damage incurred.