"We want his remains back as a family and as Ethiopians because that is not the country he was born in," Fasil Minas, one of his descendants, told a British broadcaster.
He said "it was not right" for the prince to remain buried in the U.K.
Prince Alemayehu was captured aged seven by the British Army and taken to England in 1868, arriving as an orphan after his mother died en-route.
He spent the next decade in Britain, and was looked upon kindly by Queen Victoria, who arranged for his education before his death aged 18 in 1879 from pneumonia.
At the reported request of Queen Victoria, he was entombed in the catacombs of St George's Chapel at Windsor Castle, the royal residence west of London.
Ethiopian leaders have previously asked the British royal family for his remains to be returned to his homeland, and his family told the BBC recently that they too had requested the repatriation.
But in a statement, Buckingham Palace said it was "very unlikely that it would be possible to exhume the remains without disturbing the resting place of a substantial number of others in the vicinity."