It is believed the trio was heading back to the house that Cipriani shares with a Rebels team-mate when the car failed to take a bend and went over a shrub and into a parked car. It is understood no one was injured in the accident.
Cooper, a significant factor in the Reds' drive to the Super Rugby title last season, has been recuperating from a serious knee injury he suffered playing for Australia at the Rugby World Cup last year.
Reds chief executive Jim Carmichael said he had no concerns about the talented flyhalf, who was evicted from the pub on Stradbroke Island last month after an altercation with a local man, being in Melbourne.
He was not aware of Cooper being involved in the accident. He said Cooper had travelled to Sydney to film a promotional rugby video last Wednesday and was given permission to spend the weekend in Melbourne because he was not yet ready for the Reds' opening-round game against the Waratahs in Sydney on Saturday or for the Reds' reserves.
''Until Quade Cooper does something that isn't right, I take the view that they are … still young men who go out,'' Carmichael said.