They include demands for the return of artworks by Lucas Cranach the Elder, Adolph von Menzel and Friedrich Tischbein, and the "New Cabinet", one of the most intricate pieces of furniture produced by David Roentgen, the 18th century master craftsman.The family has yet to comment on reports it is also demanding the right to live rent-free in the former royal residence of Cecilienhof Palace, the site of the 1945 Potsdam Conference, which today is a museum.
"Contrary to various reports, the House's primary objective is to maintain the collections in existing museums and continue to make them available to the public... Speculation that museums would be forced to close can therefore be dismissed as utter nonsense," a lawyer for the family told The Daily Telegraph.
The House of Hohenzollern fell after the First World War. Wilhelm II abdicated and went into exile and the family was forced to give up its main palaces. But it retained ownership of many lesser residences and artworks which it later lost after the Second World War - it is these the family is now trying to reclaim.
Most of the family's possessions were in the Russian zone of occupation which later became East Germany, and were expropriated by the communist authorities. The family is pursuing a claim under German laws that mandate the restitution of property seized under communist rule.
Opponents say the former royals are not eligible under the law because of a clause that excludes those closely involved with the Nazi regime.
Crown Prince Wilhelm, the former Kaiser's son, allied himself to Hitler in the Thirties in an attempt to restore the family's fortunes.
"At the moment, the positions of the negotiating parties are still very far apart," the German culture ministry said in a statement at the weekend.