The Portuguese, who won the Premier League with Chelsea in 2005 and 2006, has made clear his desire to return to England after finishing his job in the Spanish capital.
And the former Tottenham boss is confident that Mourinho's winning mentality makes him the right man to succeed the Red Devils hero, who reached his 26th anniversary in the Old Trafford dugout in November.
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"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."
Given Sir Alex's vast trophy cabinet over a quarter-century in charge at Old Trafford, the ex-Spurs manager noted that it would be a daunting task for any successor, making Mourinho more of a unique candidate to take it on successfully.
"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," Redknapp continued.
"Taking over from Fergie, whenever it happens, will also be almost impossible but Jose could once again be the special one. If anyone could do it, he could, and United fans would love him."