O'Sullivan, 38, had lost 18-14 to Selby at the Crucible in Sheffield and was returning to his home in East London with his six-year-old son Ronnie Jr.
According to the report the pair "dramatically cheated death" and had to be scrambled from the wreckage.
In slippery conditions, O'Sullivan's car came off the M1 and hit the central reservation,.
Both father and son were unhurt and left only "shaken" by the crash which happened at around 1:30am.
The Mirror claimed a source said that the weather was "poor" but that speed was not a factor.
Earlier O'Sullivan had been in reflective mood after his defeat to Selby.
He said he had "never been in such a good place" despite the defeat.
"He out-fought me, out-battled me and I’ve got no complaints. I fought my hardest," said O'Sullivan.
“That’s the nature of sport. If you buy a raffle ticket and sign up to be a sportsman you accept the losses as well as the wins. You can’t have it all your own way all the time. I’ve had some great wins here but losing is part of the sport and you accept it. You have to go away, lick your wounds and try and go one better next time."