Clooney, whose new movie The Monuments Men tackles the issue of stolen art works, stood by his view that the UK should follow the example of the Vatican and the US's Getty Museum by giving back the relics.
The American actor accepted that people may take the view that as an outsider, he did not know enough about the situation, but he said he thought it was "probably a good idea" for them to be returned.
Clooney was recently asked by a Greek journalist if he thought the 2,500-year-old sculptures - taken from the Parthenon in the early 19th century by the Earl of Elgin and now housed at the British Museum - should be returned to Athens.
Speaking at a press conference at the National Gallery today, he said: "I stepped into one the other day, I was at a press conference and somebody brought it up. So I did a little research to make sure I wasn't completely out of my mind, and even in England the polling is in favour of returning the marbles.
"The Vatican returned parts of it, the Getty (Museum) returned parts of it. It is a question in that case of breaking up one piece of art, and whether that piece of art can be as best as possible put back together. So it's an argument to say, maybe that's one of those instances."
Clooney - the writer, director and star of the new film about a special troupe of soldiers on a mission to recover and return art stolen by the Nazis from Europe in the Second World War - went on: "There's certain pieces that you look at and think that actually would probably be the right thing to do.
"I know someone yesterday said, 'He's an American and he doesn't understand'. Well he's probably right.
"But I do think its worth having an open discussion about. I said it's probably a good idea if they found their way back."
His co-star Bill Murray agreed, joking the art had had a "nice stay" in London.
"It seems like it's a problem all over the world," said the Lost In Translation and Ghostbusters star.
"Who wins this art and where did it come from and do they have the right to get it back. It's had a very nice stay here, certainly, but London's gotten crowded and there's plenty of room back there in Greece.
"England could take the lead on this kind of thing - letting art go back where it came from. And then if they were all together, the Greeks are nothing but generous, they'd loan it back once in a while like people do with art, right?"
The Monuments Men, which also stars John Goodman, Bob Balaban, Jean Dujardin, Hugh Bonneville and Cate Blanchett, is based on the true story of the team of art experts who entered the war with the objective of saving Europe's greatest art and buildings.
But Clooney and his fellow screenwriter Grant Heslov admitted they had taken a little poetic licence with the story, and they chose to change the name of The Monuments Men involved in the film.
Clooney said: "We wanted to change the names, because we wanted to be able to tell a story. We weren't doing a documentary, we didn't want to give any of these real men flaws that would be upsetting to their families. We wanted our ability to be able to tell a story without offending anyone."
The Monuments Men opens in cinemas on Friday.