United legend Giggs has been combining his role as a player at Old Trafford with coaching duties in the wake of David Moyes' dismissal.
He will remain in charge of first-team affairs until the end of the season, with a decision then set to be taken on a long-term appointment.
Netherlands boss Louis van Gaal is considered to be a leading candidate to inherit the reins, but former United defender May feels there will always be a role for Giggs.
He told Sky Sports News Radio: "I honestly think that Giggsy will be there next year. I hope he's there next year because Manchester United need people of Giggsy's calibre and experience and knowledge of the club.
"I'm sure whoever comes in will keep Giggsy on board and press on for some success next season.
"You've got Giggsy, Scholesy and Nicky Butt there who have a wealth of experience - Phil Neville as well. I'm sure whoever comes in, they don't need to look any further than those four players for experience and knowing how the club actually works."
May is convinced that it will be Van Gaal who gets the nod, with it important that United find someone with a proven track record at the very highest level.
He added: "Everything I've heard is all about Van Gaal and bringing in his own backroom staff. At the moment, I can only see Van Gaal coming in.
"He's someone who has done big things at big clubs, he's very experienced and United need somebody of that winning way. He ticks all of the boxes."
While such a move would raise questions over Giggs' future, May sees no reason why the Welshman could not take his United playing career into a 25th season.
He said: "I think he is still good enough. There have been many games this season where he has been United's best player, even at the age of 40.
"Maybe the manager could pick and choose his games. Whatever happens, it would be a loss to the Premier League and Man United if Giggsy does decide to retire because he has been absolutely incredible over the years."
It has been suggested that a run-out against Hull City in a 3-1 win on Tuesday could be Giggs' last at Old Trafford, with that contest offering a glimpse of what United's future could hold.
Teenager James Wilson and 20-year-old Tom Lawrence were handed their Premier League bows by Giggs - with Wilson netting twice - and May feels whoever is around next season will look to mix exciting academy graduates with experienced new arrivals.
He said: "There is young talent at the club, of course there is, but I feel they do also need to bring in experienced players to bring United back to where they deserve and where they should be.
"The main thing is that United keep doing what they are doing, keep producing the young kids. Whether it's Van Gaal or whether it's someone else, United have a tradition of doing that.
"With Financial Fair Play coming into it, it's important that the youth players come in and contribute to the first team, as they have in the last few years."