Clooney was on the island shooting his new series Catch-22.
According to the site, George was said to be hit by a auto which suddenly changed direction at a spot close to a hotel.
According to NBC reporter Claudio Lavanga, the Sardinia hospital where Clooney was being treated has already discharged the actor.
It was announced in April that the multi-talented star was reducing his role in the Hulu production so he could concentrate on his directing and producing credits.
Clooney, 57, plays US Air Force commander Scheisskopf in the World War Two Channel 4 drama, based on Joseph Heller's classic novel.
Immediately after the crash, Clooney was transported to a nearby hospital.
Even earlier in June, Clooney was seen zipping around the island on a scooter with Amal, 40, hugging him tightly.
They all came together at the up-market Il Marino di Puntaldia restaurants after George had finished filming.
It was from that moment George made it his mission to land Amal, later taking her on their first date at a plush London restaurant.
Clooney has a home with his wife, human rights lawyer Amal, on the Italian mainland, on Lake Como.