Redknapp wrote in The Sun: "I spoke to David on Thursday night â€” it was just a quick chat to wish him well.
"We didnâ€™t go into much detail but I donâ€™t think the job could have gone to anyone better. Itâ€™s his dream job.
"He has respect from everyone around the game and is the right man for the job.
"And heâ€™s British which I find particularly pleasing. Thereâ€™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 â€” and the trigger-happy chairmen â€” 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 â€” manage."