There has been frenzied talk about the forward's future at Old Trafford with some reports suggesting he could be on his way out the door this summer.
But former skipper Robson has urged Rooney to 'see sense' and stay put with the Premier League champions.
"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."