The former Red Devils captain believes the Welshman can become a brilliant coach and could act as United's version of Pep Guardiola.
The Spaniard, currently in charge at Bayern Munich, stepped into management almost straight after he ended his playing career and became one of Barcelona's most successful coaches following his time spent at the Camp Nou as a player.
Robson is of the belief Giggs can do the same and has implored the Old Trafford outfit to look beyond Jose Mourinho and install the former attacking midfielder as Louis van Gaal's replacement.
"Ryan really can be the Guardiola of United, I am sure of it," Robson told The Sun.
"Yes, he's a quiet lad but that should make no difference. He has always been a deep thinker on the game. He's worked hard to get to this point.
"They talk about Guardiola being intelligent and having a great football brain. Ryan is no different. He just needs the chance to prove what he can do once Van Gaal goes.
"There should be no knee-jerk reaction, no panic. Guardiola has a great record but United should not be reacting to what happens at City. United should carry on what was started when Van Gaal arrived.
"It was always said that during Van Gaal's time as manager Ryan would learn under him, get his pro-licence and be ready for the job. That should still be the case.
"People say Ryan hasn't got the experience. But he watched how Sir Alex Ferguson worked for 26 years and he's watching Van Gaal go about things now.
"He represents United's soul. He has been at the club since he was 13 and knows what is expected."