Welsh midfielder Giggs is currently caretaker boss at Old Trafford following the recent sacking of David Moyes which has prompted fans to call for him to get the job on a full-time basis.
It appears, however, that Holland national team manager Louis van Gaal will land the United role - a move Robson backs - but he wants to make sure that the current coaches remain in the dugout to keep a United touch on the sidelines.
"I think it would be very disappointing for those lads not to be kept on, in whatever role, as they are part of Manchester United," Robson told MUTV.
"The fans would be very disappointed if they don't have a future in the club.
"I have read that van Gaal wants to bring in a goalkeeper coach, a fitness coach, and (Patrick) Kluivert as his assistant.
"If you are talking about bringing all these people in you have to make sure that you are making the right decision and you are not allowing them too much rope.
"It is up to the board to step in and say 'you can have leeway with this, but there are definitely restrictions on this part of the club'.
"That has to come from the club rather than the new coach. Sometimes I think when you go into a new club, why not give the staff a chance?"
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