Citing an anonymous source, news site Page Six said the actor was sick of being photographed by paparazzi every time he and his wife, British human rights lawyer Amal, stay in the villa in the town of Laglio.
“George loves the area and the people who live there, but is conscious of the attention he gets when he is in town,” the source told the news site.
According to the source, Clooney is considering accepting an offer of 100 million dollars for the 18th century mansion (about €90 million), almost ten times the amount the actor paid for the property back in 2002.
“He has received a huge offer for the villa, which he is considering, and he would buy another, less accessible property in another area of Italy,” said the source.
Since the article was published on Wednesday, the Italian media has been awash with rumours of Clooney's departure from Laglio, where he is an honorary citizen.
SEE ALSO: George Clooney: the treasure of Laglio
Privacy has been a constant concern for the actor since he moved to the town.
Earlier this week, the star was photographed shirtless as he watched the sunset with Amal and a friend days after the couple were snapped as they said goodbye to fellow Hollywood actor Robert De Niro and his wife Grace Hightower.
In April the mayor of Laglio Roberto Pozzi made it illegal for anyone to approach Villa Oleandra and Clooney's adjoining property, Villa Margherita, following complaints from the star.
Anyone caught coming within 100 metres of the villas, either by water or by road, faces a fine of up to €500.