While it still unclear what prompted United Chief Ed Woodward to sign Solskjaer as United manager after sacking Mourinho, many have viewed the decision as well thought for.
The Red Devils have improved drastically in the time since, making the quarter-finals of the Champions League and moving to within two points of the top four.
Manchester United have recently hit a rough patch, though, with back to back defeats to Arsenal and Wolves stopping the Ole Gunnar Solskjaer momentum.
Redknapp believes the Norwegian should have been named as the club’s permanent replacement for Mourinho after the 3-1 Champions League win over PSG earlier this month.
And he also reckons that Woodward never envisaged Solskjaer becoming such a strong contender for the United job on a full-time basis.
“When he recruited Solskjaer from Molde in December, Ed Woodward could not have imagined that four months on he would be a serious contender for the job,” he told the Daily Mail.
“Solskjaer has more than exceeded expectations, propelling United into contention for the top four and getting them through to the quarter-finals of the Champions League against all odds.
“He has made a group of players who were performing well below par look like the multimillion-pound assets they truly are.
“He clearly has the support of his players, many of whom have gone on the record saying he should be appointed full-time.
“Solskjaer will feel he has more than proved himself but the longer United wait, the greater the risk that the feelgood factor begins to fade.
“His team have suffered two poor defeats by Arsenal and Wolves, with Saturday’s FA Cup exit ending their best chance of winning a trophy.
“United are still to face Chelsea and Manchester City at home in a tricky run-in and have to go back to Molineux, too.
“Should this dip become a slump, United finish outside the top four and fail to win the Champions League, they will not ride into next season on a wave of positivity.
“There would surely be question marks over whether Solskjaer could challenge City and Liverpool for the title.
“Matters have been complicated by the return of Zinedine Zidane to Real Madrid. Now that door has closed to Mauricio Pochettino, United are in pole position to try to tempt him away from Tottenham.
“Pochettino was the No 1 candidate to replace Jose Mourinho.
“He has an outstanding track record when it comes to improving players and has established Spurs as a top-four side, despite having his hands tied in the last two transfer windows.
“Regardless of Tottenham’s recent poor run of form, he remains the strongest candidate and would become an even more attractive option should United’s season not finish on a high.”
United are next in action after the international break, where they will face Watford on 30 March.
They then face Wolves just three days later before a mouthwatering showdown with Barcelona on April 10.