Photographs suggest that the former England captain crashed into another vehicle as he pulled out of his Beverley Hills home. Brooklyn, meanwhile, was pictured in the front passenger seat.
David's black Range Rover Sport, which is estimated to cost up to £47,000, hit an oncoming white Acura 4x4 which was being driven by a blonde woman.
"There was an incident on Friday between David and a woman driving a car," an insider told Sky News. "No one was hurt and there was no need for drivers to exchange details."
The front bumper of David's car appeared to have been torn away in the impact, while the white car suffered a side dent.
David reportedly picked up pieces of debris and reversed back into his driveway, as he waited for police to come and inspect the damage, and speak to other eyewitnesses.
This is not the first time that David and Brooklyn have been involved in a car crash.
The father-son duo had a lucky escape in 2011 after their Cadillac Escalade was the third to be sandwiched in a pile-up on a busy motorway in Los Angeles. Fortunately David and Brooklyn, who were both wearing seatbelts, were left unhurt.