An agreement by which the sculptures from the Parthenon could be returned to Greece is "close", a former adviser to the government of this Balkan country told the BBC.
Professor Irena Stamatudi said "negotiations appear to have progressed" over the relocation of the antiquities, also known as the Elgin Marbles, which were taken from Athens more than 200 years ago and are on display at the British Museum.
These claims come ahead of a meeting between British Prime Minister Keir Starmer and his Greek counterpart in London.
Sculptures were not discussed at the beginning of the meeting, the British Prime Minister's office announced.
The meeting comes as reports indicate that talks have recently advanced on an agreement to transfer the statues to Athens.
The status of the sculptures has been the cause of diplomatic tensions between Great Britain and Greece for decades.
Greece says they were stolen, but the British Museum rejects this and says they were obtained legally.
Negotiations between Greece and the British Museum continue from 2021.
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Professor Stamatoudi, an adviser to the Greek culture minister during previous negotiations over the Elgin marble, told BBC Radio 4 that she believed "a deal is close" but was not sure if it was "close enough".
She says the Greek government has proposed a "cultural, strategic partnership" that would involve sending other antiquities to the British Museum to fill the gallery left empty by the return of the exhibits.
Negotiations about what could be sent to the British Museum are "secret," Stamatudi said, adding that while she is not involved in the ongoing negotiations, she believes it would include "antiquities that attract public attention."
Professor Stamatudi added that ensuring the return of the sculptures is something "all Greeks are passionate about" because antiquities are widely considered part of the country's "cultural heritage".
Greek Prime Minister Kyriakos Mitsotakis has made the return of lion sculptures a political priority for the country.
The issue sparked a diplomatic row last year when then-British Prime Minister Rishi Sunak canceled a planned meeting with Mitsotakis after his Greek counterpart indicated he would use their meeting to raise the issue.
The previous government said the sculptures should remain in the museum.
In contrast, Labour's position was that they would not stand in the way of an agreement between the British Museum and Athens on the loan, should it be agreed.
Government sources in Athens have told Greek media that Mitsotakis wants to "rekindle the issue" with Starmer after the two prime ministers meet in November 2023.
Earlier this week, Greek government spokesman Pavlos Marinakis said Mitsotakis would raise the issue with Starmer again, but that it was more a matter for the British Museum than the government.
He also denied a Sky News report that three private meetings had taken place between senior Greek officials and members of the British Museum's board of directors.
Downing Street said Starmer told the Greek prime minister he hoped to "build on our strong bilateral relationship and discuss common issues", while Mitsotakis said Greece and the UK would strengthen their relationship during "turbulent times".

Starmer is understood to be more open to moving the statues than his predecessor, provided the Greek governments and the British Museum reach an agreement.
The Elgin Marbles were made in the fifth century BC and were originally displayed in the Parthenon in Athens.
It is considered to be one of the most valued antiques from the period of ancient Greece.
They were taken by the British aristocrat Lord Elgin while Athens was part of the Ottoman Empire and were badly damaged on the way to London, where they have been on display ever since.
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