Public broadcaster ARD said it had obtained lists of the human remains that are still held by the Prussian Cultural Heritage Foundation, which administers the capital's state museums.
The Prussian Cultural Heritage Foundation is responsible for the collections at Berlin's world-famous museum island, as well as the Berlin State Library and the Prussian Secret State Archives.
Most of the skulls and bones are marked as stemming from Germany's former East African colonies, including 1,003 items from Rwanda and 60 from Tanzania. Among them are 10 skulls of children.
Some of the human remains, kept at the Foundation's main storage facility, came from insurgents who had been decapitated by German troops. Their skulls were then sent to Berlin for "scientific" experiments.
Asked about the items, the foundation's chief, Hermann Parzinger, told ARD that his organisation "has no problem with returning these things".
Germany has in recent years handed back 20 skulls belonging to indigenous Namibians.
The skulls are among an estimated 300 taken to Germany after a slaughter of indigenous Namibians during an anti-colonial uprising in what was then called South West Africa, which Berlin ruled from 1884 to 1915.
The skulls gathered dust in the German archives until 2008, when ARD reported that they were still kept at the Medical History Museum of the Charite hospital in Berlin, and at Freiburg University in the southwest.
The publicity prompted Namibia to seek the restitution of the remains.