Redknapp wrote in The Sun: "I spoke to David on Thursday night - it was just a quick chat to wish him well.
"We didn't go into much detail but I don't think the job could have gone to anyone better. It's his dream job.
"He has respect from everyone around the game and is the right man for the job.
"And he's British which I find particularly pleasing. There's no way he will serve the 27 years that Alex Ferguson has.
"Those days are gone forever.
"But I hope that even with the demands of the modern-day game - and the trigger-happy chairmen - that Manchester United take us back to the future.
"And remind us that you can still give a manager the time to do what he does best - manage."