La Nuova Sardegna said the 57-year-old was headed to a film set on Tuesday when his motorbike was hit by a auto.
He is understood to have received treatment at John Paul II hospital, but NBC News report that he has since been discharged. They also claim it is not believed his condition is serious.
George relocated his family to the idyllic Italian island for the summer to direct the forthcoming TV mini series.
The paper also tweeted a photo of his scooter abandoned by the side of the road with a Mercedes estate vehicle just feet away.
On close inspection it is clear that the windscreen is smashed, which might have been caused by the incident. More information is to follow.
The couple had previously been enjoying their European trip alongside George's parents Nina and Nick Clooney, as well as Amal's mother Baria Alamuddin.
Clooney has a home with his wife, human rights lawyer Amal, on the Italian mainland, on Lake Como.
The story, set in Italy during World War 2, focuses on Christopher Abbott's character of Yossarian, a US Air Force bombardier who is furious because the bureaucratic rule known as Catch-22.