The former Red Devils captain believes the want-away England international has an important part to play under new manager David Moyes at Old Trafford next season
Rooney was left out of Sir Alex Ferguson's squads for the last two matches of the Premier League season having asked to leave the club.
Robson, however, believes there is nowhere better for the England striker to go and is convinced he would play an important part for the English champions under David Moyes.
"There was a bit of a problem towards the end of the season with Wayne and Sir Alex, but I just hope Wayne sees sense," Robson told Sky Sports.
"There's no better club than this club and if David Moyes does say that he wants Wayne to stay, I'd love to see him playing for Manchester United again next season because he's a great player.
"He's a real asset to the club and I'd like to see him stay for many more years."