By ESPNSTAR.com staff
Ferguson has been at the helm of the Manchester giants for 26 years, winning 12 Premier League titles and two Champions League trophies during that period.
He had a fierce rivalry with Mourinho during the latter's time in charge of Chelsea in the previous decade but is known to have great respect for Mourinho's managerial talents.
Mourinho has the record of having won the domestic title in four European leagues with Porto, Inter Milan, Chelsea and Real Madrid. He has also made his desire to return to England in the future publicly known and many have speculated that United would be his favoured destination.
Redknapp concurs with such a theory, writing in the Sun, "It is hardly the greatest secret that Jose is planning - one day - to manage again in the Premier League and it wouldn't surprise me if he ends up in Manchester. But I can picture him being at United rather than City."
"When Alex Ferguson eventually calls time on his amazing career, there will not be many serious contenders to take over.
"But Jose, I have no doubt, would be big enough to take on the ultimate challenge and succeed the greatest manager this country has ever seen.
"He would be amazing at Old Trafford. His style would be very different to Fergie's but I'm sure he would get the same amount of success.
"Attempting to manage this great club has broken many managers. Look at when Sir Matt Busby left Old Trafford. The likes of Frank O'Farrell and Wilf McGuinness really struggled as it was virtually an impossible job.
"But Jose could once again be the special one. If anyone could do it, he could - and United fans would love him.
"I have missed him since he left the Premier League as he added star quality. He's not everyone's cup of tea, but I've always liked him.
"When he came to Chelsea, he was like a breath of fresh air. He was exciting, brash and cocky. People loved him or hated him. Chelsea fans certainly adored him.
"Lots of people, including some managers, wanted to see him fall flat on his face but it didn't happen.
"He had not been a professional footballer but he proved this is no longer required. He simply worked very hard to get to the top.
"I remember talking to Frank Lampard about him and he thought he was fantastic. He helped Frank feel 10ft tall.
"Jose told him: "You're one of the greatest midfielders in the world" and he responded.
"Although he has always been lucky enough to manage good players, he has always got the best out of them.
"Not all coaches can do that. Before joining Real, Jose did incredibly well at Inter Milan and look at them since. They have not been near a thing."
The former Portsmouth manager also said that he was looking forward to the crucial Champions League clash between Manchester City and Real Madrid on Wednesday. City are the bottom of Group D and need to win their remaining two games against Real and Borussia Dortmund.
"[He] returns to England this week for Real Madrid's Champions League match away to Manchester City," Redknapp observed.
"City need a miracle to reach the knockout stages of the Champions League, while Real still have work to do. It has been a poor European campaign for Roberto Mancini's side but you have to take into account what an incredibly difficult group they were placed in.
"But seeing Real will be great. Ronaldo will be returning to Manchester, while I'm hoping Luka Modric plays."