A picture from La Nuova suggests that Clooney hit a auto while on the motorway.
The actor was reportedly taken to the emergency room of the John Paul II (Giovanni Paolo II) hospital, which is in Olbia, Sardinia.
The newspaper tweeted a photo apparently from the scene, showing a lightly smashed up motorbike and auto, with a caption suggesting the vehicle had been turning and Clooney had made contact with its windscreen.
A fire extinguisher can be seen on the road but no people are visible.
HuffPost UK has contacted George's representatives for comment.
Mr Clooney was driving from his rented villa in Punta Aldia to Capo Ceraso, on the Sardinian coast, where he is filming a TV series based on the Second World War novel Catch-22.
This is a developing story and will be updated when more information becomes available.
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The couple have also been joined by George's parents, Nina and Nick Clooney, and Amal's mother Baria Alamuddin.
Local police are investigating the accident, Ansa said.
The stunning abode features two swimming pools, a tennis court and an incredibly colourful landscape.
They met when she attended one of his parties at his Lake Como mansion, and Wednesday in Venice a year later.
The move comes after it was announced in April that the actor was going to be reducing his role in the production so that he could concentrate on directing and producing.
His castmates include Hugh Laurie, Austin Stowell ('Whiplash') and Kyle Martin Chandler ('Friday Night Lights').