The former Wales international winger has been put in charge of the first team until the end of the season following the dismissal of David Moyes on Tuesday.
"He could be," said Robson when asked if Giggs could be the United manager at some point in the future. "It's up to Ryan to go out and prove himself. I have not actually seen Ryan coach and that's a different ball game.
"Pep Guardiola came through the ranks at Barcelona and then got a chance [as manager] and was very successful. Ryan is a strong man but whether he is a good coach, or whether he can delegate to bring in good coaches underneath him, only time will tell.
"I don't know what the club's feelings are about Ryan but I think they will probably go with a more experienced type of coach who has been at big clubs and done it at big clubs."
Robson is considered a United legend, having played for the Red Devils between 1981 and 1994, winning the Premier League twice and the FA Cup on three occasions during that period.