Redknapp feels that Giggs's knowledge of the club and the respect he commands from the players means that he is the perfect man for the job.
"From his first press conference to walking out as United boss at Old Trafford, Ryan Giggs has meant business. He looks every inch a Man United manager," he wrote in his column for the Daily Mail.
"Nobody knows that club better than Giggs and if United really want to build for the future then why not give him the chance to do it?
"He has won everything there is to win as a player and you could tell he had the respect of the players on Saturday. They looked like they were enjoying playing for him."
Giggs has made 962 appearances for United since making his debut in 1991.