England international Rooney has recently been linked with a move away from Old Trafford and despite manager Sir Alex Ferguson having dismissed that speculation, the 27-year-old reportedly still harbours doubts over his future at the club.
However, Robson has stated his belief that Rooney will go on to have a similar career to Giggs, who has made 932 appearances for the Red Devils since his debut in March 1991.
"[Rooney has] got a long-term contract at United and for me his future is at this club. I think he's proved it anyway," Robson told BBC Sport. "It's seven or eight years that Wayne's been here and he could be more or less like another Ryan Giggs as far as I'm concerned."
Rooney joined United in 2004 from his boyhood team Everton.