The forward was leaving United’s Carrington training base when his £700,000 Rolls-Royce collided with a traffic island, The Sun reported.
The incident happened just hours after United beat Burnley 1-0 at Turf Moor.
Rashford was shaken but not hurt following the accident, the newspaper added.
Photos posted on social media showed a dent to the car and the road littered with debris.
Police were called to Carrington Spur but no arrests were made and no ambulances were called.
Rashford’s teammate Bruno Fernandes is said to have urgently stopped to help after driving past the scene.
The Standard has contacted Greater Manchester Police and representatives of Rashford for comment.
Rashford reportedly owns three Rolls-Royces - the £700,000 Black Badge Wraith involved in the crash, a £390,000 Black Badge Cullinan and a £560,000 Cullinan Blue Shadow.
Speaking before the match, Rashford said that a win would be a “game-changer” for the club. Man Utd had lost their previous three games.
“It’s a difficult position and I’m not as happy as I’d like to be, but there’s only one way to get back this happiness is to seek results.”
“We know the effect that a victory can have on the team and then it’s up to the players to show consistency. That’s what we lacked. Last year, we were very consistent at home, but very irregular away.”