The gallery on the city's South Side is facing a legal wrangle with the family of Emma Budge, a Jewish woman whose collection was sold under duress in Berlin in the 1930s.
The Burrell Collection - which is run by Glasgow Life, the city council's arm's length art and culture division - has been served with a spoilation claim by Emma Budge's heirs.
It was served via the UK Department for Culture, Media and Sport's Spoilation Advisory Panel, which was set up to investigate claims of people who lost rare art at Nazi hands.
A spokesman for Glasgow Life said: "We are offering every assistance to the Department for Culture, Media and Sport's Spoilation Advisory Panel.
"However, while the inquiry is ongoing it would be inappropriate to comment before evidence is presented."
The item being claimed by Emma Budge's heirs is a tapestry called The Visitation, which has been at the Burrell Collection for more than 70 years.
A German lawyer representing the heirs was reported to have said the work should be returned and that museums should not have "stigmatised" artefacts in their collections.
The Nazis stole or forced the sale of huge quantities of valuable works of art, selling them to collections around the world.