The British Museum is engaged in "constructive discussions" over the possible return of the so-called Elgin Marbles in an exchange with Greece.
Last year it emerged negotiations between Greek authorities and the museum chairman, former Tory austerity Chancellor George Osborne, over the 2,500-year-old cultural treasures were at an "advanced stage".
The sculptures could now be loaned to Athens under a long-term "cultural exchange" programme, according to the Daily Telegraph, as UK law prevents museums from giving away artefacts.
It is unlikely any of the cultural treasures will be shipped immediately and may first only see a proportion of the objects sent, the report claimed.
The UK is engaged in a long-running dispute with Greece over the legal ownership of the 17 sculptures and part of a frieze that once decorated Parthenon temple at the Acropolis.
The artefacts were removed from the temple in Athens in the early 19th century by the British diplomat, Lord Elgin.
The Greek Prime Minister Kyriakos Mitsotakis has previously said they were "stolen" and belong in the Acropolis Museum.
He has even offered to lend some of his country's other treasures to the British Museum in exchange.
A spokesman for the British Museum said: "We've said publicly we're actively seeking a new Parthenon partnership with our friends in Greece and as we enter a new year constructive discussions are on-going".
Last month, the museum said it has "publicly called for a new Parthenon partnership with Greece" and will "talk to anyone, including the Greek government, about how to take that forward".
It added: "We operate within the law and we're not going to dismantle our great collection as it tells a unique story of our common humanity.
"But we are seeking new positive, long-term partnerships with countries and communities around the world, and that of course includes Greece."
A Department for Digital, Culture, Media and Sport spokesman said: "The Parthenon Sculptures in the British Museum are legally owned by the trustees of the British Museum, which is operationally independent of Government.
"Decisions relating to the care and management of its collections are a matter for the trustees".
