Giggs has been placed in temporary charge of United following the dismissal of David Moyes, who was fired just 10 months into his six-year contract.
Although Saturday's 1-0 defeat to Sunderland reminded United fans of the current squad's faults, the interim appointment of Giggs, along with coaches Paul Scholes and Nicky Butt, has raised morale at the club.
There is a growing feeling within the dressing room that Giggs should be given the job full-time, but the United board want a more experienced candidate so they have turned to Van Gaal.
The Holland coach is expected to be appointed this week, and Robson feels the 62-year-old must include Giggs and his former 'Class of '92' graduates in his plans.
"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?"
With Pep Guardiola, Jurgen Klopp and Carlo Ancelotti having all ruled out coming to United, Van Gaal remains the only obvious choice to lead United next season.
United have always maintained the fact that Van Gaal will not be able to take over fully until after the World Cup is not a problem.
Holland's World Cup preparations begin on Wednesday when the Eredivisie-based players in Van Gaal's squad meet for their first training camp in Hoenderloo, which is 50 miles to the south-east of Amsterdam.
The cameras will focus on the Holland manager, but he has chosen not to hold his press conference until May 13, when he will announce his provisional 30-man squad for the finals in Brazil.
The fact that the squad does not meet up until Wednesday afternoon leaves open the possibility of Van Gaal attending United's final home match of the season against Hull on Tuesday night.
The shock defeat to Sunderland was United's seventh on their own patch in what has been a dismal year.
Juan Mata feels the players owe the supporters a much better performance against Hull.
"I was unhappy with the result, but the good thing is that on Tuesday we play again in Old Trafford," United's club-record signing wrote on 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."
The Hull game will be a significant one for a number of reasons.
Nemanja Vidic will play his final game at Old Trafford. For Rio Ferdinand and Patrice Evra - both of whom are out of contract this summer - it could be their last home game too.
And it may well be the last time United fans get a glimpse of Giggs for a while as he has not been assured that he will figure in Van Gaal's plans - either as a player or coach.
The interim boss did not rule out naming himself in the matchday squad when quizzed on the matter at the weekend.
Striker Wayne Rooney could return after missing the Sunderland defeat due to illness and a tight groin.