There was no immediate confirmation from his Red Bull Honda team or the hospital treating him. A spokeswoman for Cesena's Maurizio Bufalini hospital said a statement was expected later.
Hayden, 35, was struck by a car while training on his bicycle along Italy's Adriatic Coast, the force of the impact shattering the car windscreen.
The last medical bulletin from the hospital, dated May 20, said Hayden remained in a critical condition. The hospital had previously said he had suffered serious brain damage in the accident.
Doctors had placed the 2006 MotoGP champion, known as "The Kentucky Kid," into a medically induced coma. Hayden's fiancee, Jackie, was joined at his bedside by his brother Tommy and mother, Rose, who flew in from the United States.
Hayden last raced in the MotoGP championship in Spain in September 2016 as a stand-in for injured Australian Jack Miller at the privately-run Marc VDS Honda team. He started 216 races between 2003 and 2015, winning three.
Italian newspapers reported on Monday that investigators had found video of the accident from a camera on a house overlooking the road. They said the images suggested Hayden had failed to stop at an intersection and was hit full on by the passing car.
There was no immediate confirmation of the report from the investigators.
Reporting by Crispian Balmer