Guardiola has quickly established himself as one of the best managers in world football, having led Barcelona to three league titles and two Champions League trophies in an illustrious four-year stint at the club before guiding Bayern to the Bundesliga title and the Champions League semi-finals this season.
Giggs is in charge of United for the final four matches of the current campaign following the sacking of David Moyes, and a 4-0 victory over Norwich City in his first game at the helm has led to speculation that he could be handed the job on a permanent basis.
Lindegaard believes that the 40-year-old United legend would be a fine choice to take over at the club, likening him to both Guardiola and former manager Sir Alex Ferguson.
"It might sound pretty rash and naive, but, in my opinion, we are dealing with a new Guardiola. What we have seen in the first week has been more than convincing. The similarities with Sir Alex Ferguson are striking and it is evident that Ryan Giggs has learnt from one of history's most respected football managers," Lindegaard told BBC Sport.
"Some would question whether you can go from being a team-mate one day to a manager the next. Normally I would have reservations as well, but, in the case of Giggs, it is different.
"His latest speech, before the team went onto the pitch for the Norwich game, made my hairs stand on end in a way that I have only ever experienced from Sir Alex Ferguson: Do not disappoint the fans."
Despite a number of players publicly backing Giggs, Netherlands coach Louis van Gaal remains the favourite to take the reins at Old Trafford this summer.