Giggs was placed in charge of United following David Moyes' sacking on Tuesday and his team were noticeably more attack-minded in a 4-0 victory over Norwich on Saturday evening with striker Wayne Rooney hailing his manager's impact.
"It might sound pretty rash and naive, but, in my opinion, we are dealing with a new Guardiola," Lindegaard told BBC Sport.
"What we have seen in the first week has been more than convincing.
He added: "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!"