Guardiola was Barcelona's B team coach before being appointed the club's first team manager in 2008 and went on to enjoy four success-laden years in charge at Camp Nou.
He then moved on to Bayern Munich a year later but will leave the Allianz Arena for Manchester City this summer.
United, meanwhile, have been linked with a move for Jose Mourinho after a disappointing season under Louis van Gaal, but Robson believes Giggs is the man for the job.
"Ryan really can be the Guardiola of United, I am sure of it," Robson was quoted as saying by The Sun. "Yes, he's a quiet lad but that should make no difference. He has always been a deep thinker of 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.
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"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."
Ex-England skipper Robson added: "The owners will make their decision and, in terms of Mourinho, I know there have been rumours flying around. But there is no stand-out person who could do the job any better than Ryan.
"Remember, Guardiola was untried as a top-line coach before Barcelona decided to give him his chance. The only way we are going to know if Giggsy can do the job is for him to be given it."