Following the departure of David Moyes on Tuesday morning, Giggs will assume responsibility for the first team until a permanent appointment is made.
Ex-United skipper Robson told Sky Sports: "I know Ryan has got the job until the end of the season and I definitely think he’s going to be a manager, though whether he gets it full-time at a club like Manchester United is a big ask."
Giggs’ former United and Wales team-mate Clayton Blackmore believes the 40-year-old can lift the Reds for Saturday's game against Norwich.
He told MUTV: "Ryan's not had any time to work with the players and get them to play the way he wants them to play, but he will hopefully have them working hard and I think he’ll get a lift from them. It could be a tough day for Norwich.
"Ryan has everything you need to be a manager, including more coaching badges than me, and I’ve been coaching for 15 years."
Two other ex-Reds, David May and Danny Higginbotham, also gave their reactions to Giggs' appointment on the club's official TV channel.