The former United striker thinks it's time for Louis van Gaal to leave Old Trafford.
The former Red Devils forward believes that the Dutchman's time at the club has run its course, and while the People reports that some of the club's hierarchy are not convinced that the former Chelsea boss is the right man for the job, Sheringham insisted that he will get them back to the level they aspire to be at.
"You have to try and get the best. For me, Manchester United are still in among the top two or three clubs in the world. So you have to go for the top two or three managers," he told the People.
"I'd go for Mourinho, although maybe he doesn't quite fit right for the kind of club United are. But if it was him, he would make it happen, that's for sure.
"It's time to make the change."
Although van Gaal guided the club back into the Premier League's top four in his first season, the team appear to have made little progress as they now sit sixth in the table, four points adrift of the Champions League qualification spots.
And considering the amount of money that has been invested in the transfer market since the former Netherlands boss arrived, it is fair to say that the team should be doing much better than they currently are.
Mourinho has a proven track record for providing almost immediate results, and unlike van Gaal before he was given the United job in 2014, he has tasted success in the Premier League so may be the perfect person to elevate them to the top once again.