This morning's Sun claims United's American owners are keen to exploit Beckham's popularity to boost the club's profile.
The paper quotes a United source, who says: "It's something that has only been whispered at this stage but Beckham will always be part of the United family.
"He could do for us what Sir Bobby Charlton has done for us all these years.
"There are emerging markets all the time and there could come a time in the very near future when Becks' association with United would be renewed. "The club has lost Cristiano Ronaldo as a key marketing tool and Becks would help fill that void when he retires."
Beckham left United under something of a cloud in 2003 after his relationship with Sir Alex Ferguson became strained. However, he has always professed his continuing love for United, the club he supported as a boy.