Giggs has taken temporary charge of the first team following last month's departure of David Moyes, who was sacked just 10 months into his six-year contract.
His presence in the dugout has lifted morale at United and there have been calls for the fans' favourite to take the job full time, despite Saturday's 1-0 defeat to Sunderland.
But United are likely to opt for an experienced candidate, with Van Gaal reportedly set to be confirmed as the next boss this week.
Moyes was criticised for replacing much of Sir Alex Ferguson's coaching staff when he arrived and Robson believes United must take action to prevent Van Gaal from offloading Giggs and coaches Paul Scholes and Nicky Butt.
"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," the former club captain 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?"
Robson's former teammate Steve Bruce, now manager of Hull, also expects United to keep the long-serving veteran at the club in some capacity.
When asked about Giggs' future, Bruce joked: "He can come and see out his days at the KC Stadium, playing in the Europa League. If he's available on a free, I'd take him.
"It's a difficult one to call. If it is Van Gaal for United, I'm sure he'll have his own opinions. But there's always going to be a place for Ryan, I'm sure, because he's been a great.
"I'm sure they'll find a space for him somewhere. I don't think he'll leave.
"He will be treated properly, I'm convinced of that. He'll have some role to play.
"They'll not mess him about, that's for sure."
Sebastian Larsson's first-half strike condemned United to defeat at the weekend, a seventh loss at Old Trafford this season.
Midfielder Juan Mata admits United owe their supporters a much improved performance in Tuesday night's final home match against Hull City.
"I was unhappy with the result, but the good thing is that on Tuesday we play again in Old Trafford," the club-record signing wrote in his blog.
"It's our last game at home this season and we want to have a decent farewell in front of our fans, with a good game and a victory.
"They have given us remarkable support throughout the last year and that shows the greatness of the club and the loyalty of our fans in the good and, in particular, the bad moments."