The Elgin Marbles are housed in the British Museum
A spokesman for the Greek Embassy in London told BBC News Online that Culture Minister Evangelos Venizelos made a bid for a loan of the sculptures in a letter to Culture Secretary Tessa Jowell on 12 June.
There has been a long-running debate as to the future of the antiquities, with this latest row breaking out over a request for their return for the 2004 Athens Olympic Games.
But the UK Government denies that it received a "formal" offer for the Marbles and has informed Greece that the Marbles will stay in Britain. .
A spokesman for the Department for Culture, Media and Sport said: "Yes, we received a letter but it was not a formal request for the return of the Marbles.
"We responded to the letter and stated our position, which is the same as it was when the Prime Minister spoke to a Greek newspaper earlier this year - which is that the Elgin Marbles will remain in the UK."
Dr Nicos Papadakis of the Greek Embassy in London said that the offer was indeed a serious one and the response is a "disappointment" given that a dialogue about the Marbles future "should start at some point".
Mr Venizelos told reporters in the northern Greek city of Thessaloniki on Monday that he made the proposal in a letter to his British counterpart after Labour's election win in June.
"What's important is for the Marbles to return to Greece," he said, adding that in return Greece would send a series of major exhibitions to the British Museum on a "continuous basis".
The 56 sculpted friezes are housed at the British Museum, which has not been consulted about the offer.
"We haven't been approached either by the Greek Culture Minister or DCMS," a British Museum spokesman told BBC News Online.
The British Museum would have to be consulted in any possible move to loan the antiquities abroad.
The Elgin Marbles are known in Greece as the Parthenon sculptures and date from between 447 and 432 BC.
They depict the most formal religious ceremonies of ancient Athens - the Panathenaea procession.
In 1799 the British ambassador to the Ottoman Empire, Lord Elgin, removed the friezes and brought them to the UK.
The Greek Government has long fought to have the artefacts returned and remains willing to make periodical attempts to overturn Britain's consistent refusal to hand them over.
Plans are in place to create a £40m museum at the foot of the Acropolis in Athens with a space specifically for the Marbles - funded by government and EU money.
The museum is set to open in time for the 2004 Olympics.