United's reported interest in Borussia Dortmund striker Robert Lewandowski, coupled with manager Sir Alex Ferguson having substituted Rooney on a number of occasions in recent weeks, has resulted in speculation that the England international could leave Old Trafford this summer.
However, Robson has insisted that the 27-year-old still has plenty to give and with that in mind, he believes that the former Everton player should remain with United.
"At the moment people are trying to put a bit of a downer on Wayne Rooney but the last thing I would do is sell him," The Mirror quotes Robson as saying.
"He is an absolutely massive part of the club's success. In certain games he is a top, top player. He does things that other players can't do.
"For me, in the first 20 minutes against Villa, he won United the game. Everyone can go on about 'Van Persie, great goals', but Wayne's passing and intelligence were absolutely top class."
Rooney joined United back in 2004 from Everton for a reported £25m.