The incident, which is said to have caused minor damage to both vehicles, took place after the Red Devils' 2-0 win away at Swansea City in the EFL Cup on October 24.
According to The Sun, Shaw - who only passed his driving test last year - reversed his Range Rovers into the back of his teammate's car.
A source is quoted by the newspaper as saying: "Luke's concentration slipped and he clattered into Jones's car. He can afford the repair bill and there's no hard feelings. Nothing seems to be going poor Luke's way."
Former Southampton full-back Shaw played the final three minutes of the cup tie against Swansea - one of just two appearances all season after falling out of favour under boss Jose Mourinho.