Linz Mayor Franz Dobusch has recommended the painting of a woman - believed to be worth around 15 million euros ($27.7 million) - be transferred from its Lentos art gallery to the descendants of Aranka Munk, the city says.
It cites the findings of independent expert Sophie Lillie, who confirmed the painting had been seized from Munk by the Nazis after she was deported to a concentration camp where she died in 1941.
The administrative commission of Linz museums and the city council are expected to rubber stamp the decision by June.
Vienna lawyer Alfred Noll applied in 2007 for the return of the 1911 painting, which made its way into Linz's collection from an art dealer after World War II.
The legal heir, who wished to remain anonymous, has praised the decision through Mr Noll and thanked the Linz authorities.
"Although more than 60 years have gone by, the return of this family portrait is profoundly joyful. This shows Linz has become aware of its historical ... responsibility," the heir said in a statement.