The painting, one of the world's most famous artworks, has been in the Louvre in Paris since 1797.
Leonardo da Vinci painted the "Mona Lisa" in Florence between 1503 and 1506, and brought it to Paris, the Louvre says on its website. France's King Francis I came to possess it about 1518 under unclear circumstances, the Louvre said.
Clooney co-wrote and directed "The Monuments Men," about a U.S. military unit trying to save European artworks during World War II. He made his pitch for the Mona Lisa during a stop in Milan, the Hollywood Reporter said Saturday.
Matt Damon, John Goodman, Bill Murray and other actors from the film posed with Clooney in front of another Leonardo masterpiece, the fresco "The Last Supper," which features in the movie. The photo was controversial because of the fresco's fragility.
The last time the "Mona Lisa" was on display in Italy was 1913 -- after it was found in a Florence hotel room. It had been stolen two years earlier from the Louvre by an Italian who wanted the painting returned to Italy.
In 2012, 150,000 people signed petitions organized by the Italian government urging France to loan the painting to the Uffizi Gallery in Florence for a celebration of the 100th anniversary of its recovery.