Beckham - fresh from winning the MLS title - believes the Londoners should make the most of having Redknapp in charge.
He told The Sun: "Fabio is stepping down and there'll be lots of candidates as it's any person's dream.
"Yet Harry has proved himself over many years. The Tottenham team he has at the moment is exceptional.
"The way they play the game is the way everyone likes to see. It's exciting. There's young players with energy but that's also some experienced lads there.
"He is a passionate manager and that's what most player want. I was lucky to train there for a couple of months and he's great.
"He also loves pie and mash, so he went up in my estimations.
"I had always seen Harry and thought he was a manager you'd like to play under and I get that feeling from those two months. He looks after his players."