The painting is stored at the Burrell Collection
Lawyers acting for the family, who live in Germany, say the painting was the subject of a forced sale in 1936 under the Nazi regime.
The paining, which is valued at £30,000, is currently in store at Glasgow's famous Burrell Collection.
Earlier this year the city council confirmed that 232 of its works of art are on a list of suspected treasures looted by the Nazis.
The Jewish family claims that they were forced to sell the work through an auction to meet a wrongful tax demand.
Lawyers acting for family have contacted Glasgow City Council's Repatriation Working Group to put forward their case with a view to the painting being returned.
The legal team is asking for the artwork to be made subject of the Washington Conference Principles on Nazi-Confiscated Art of 1998.
If the council agrees, then it would pave the way for proceeding to begin, which end in the painting being handed over to the family in Germany.
The city council said that Sir William Burrell bought the work, which measures 33cm by 71cm, from German art dealer Julius Bohler in 1936 for £647.14s.
Probe launched
Bailie John Lynch, convener of the council's Repatriation Working group, said: "This is the only request we have received on the subject of Nazi spoliation and it will be considered fully and sensitively.
"Glasgow has a well-developed process for dealing with such requests."
Councillor Lynch said that over the next few months the group would seek expert advice before making a recommendation to the council.
He added: "We are taking this very seriously and have a great deal of sympathy for this family because of the events in the 1930s and 1940s in Nazi Germany."
Ephraim Borowsky, vice-president of the Jewish Representative Council in Glasgow, said: "There are national procedures for adjudicating these matters and we have every confidence that if the claim is substantiated the council will do the right thing."