Amal Clooney has had talks with Greek PM Antonis Samaras as part of a campaign to return the Parthenon sculptures from Britain.
Greece has hired Amal Clooney’s London law firm to ramp up its claim to the sculptures.
The 5th Century BC treasures, known as the Elgin Marbles in the UK, are kept in the British Museum in London.
Fellow lawyer Norman Palmer said he hoped a “conciliatory and amicable resolution” could be found.
“If it cannot, then other considerations will have to be examined,” he added.
The marbles – depicting gods, men and monsters – were removed from the Parthenon in Athens in 1811 by Lord Elgin, the British ambassador to the Ottoman Empire, which controlled Greece at the time.
George Clooney’s new wife and her colleagues from Doughty Street Chambers in London were visiting the Parthenon on October 15 after taking part in a news conference with Culture Minister Costas Tassoulas.
Costas Tassoulas told reporters his country was campaigning to have the marbles returned in the name of Greece but also “in the name of world heritage”.
Greece maintains the marbles were illegally removed and should be returned for display in a new Athens museum.
However, the British Museum and British government reject the argument.
A leading Oxford expert on classical archaeology, John Boardman, recently warned that such a move would set an “appalling precedent” for the British Museum and museums like it.
Correspondents say the hiring of Amal Clooney will raise the profile of the Greek campaign.
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