As the record goalscorer in Premier League history, Shearer's views carry a lot of weight.
The BBC pundit, who scored 313 goals in 622 career games for club and country, used his latest column on Coral to have his say on speculation Mourinho could replace under pressure Louis van Gaal at Old Trafford.
Chelsea strode to an easy 3-0 win over Sunderland in the first game since the Portuguese was sacked while the Red Devils were beaten 2-1 at home by Norwich City.
Van Gaal has been criticised by some supporters for his side's style of play, and the Norwich defeat meant United have gone six games in all competitions without victory for the first time since 1998.
'I don't think it will be long until he's back'
It leaves the Reds outside the Champions League places on goal difference and Shearer - who once famously turned down a move to United - says he will not be surprised to see Mourinho appointed van Gaal's successor.
"There is bound to be pressure on managers of big football clubs, especially in the Premier League as Mourinho has already said he wants to stay in the league and he does not want a rest," Shearer wrote in his Coral column.
"I would not be shocked if Mourinho was to manage Manchester United next, he’s favourite in the betting to do so for a reason.
"United will be after a world-class manager if they do choose to let Louis van Gaal go.
"This will only put extra pressure on the Dutchman with the United board knowing that Mourinho is available.
"I don’t think it will be long before he is back in the game. Either way, he’ll end up at a massive football club next."
Fears over style and antics
It seems strange that there would be any question marks over a manager of Mourinho's calibre taking over a struggling Manchester United.
But that reluctance, certainly on behalf of a large section of the Red Devils' support, comes from a wariness over the former Real Madrid manager's style of football and antics.
According to the Guardian, United want assurances from Mourinho that he understands the club’s traditions and is willing to fall into line if they decide that the former Chelsea manager should take over.
The paper reports that there are concerns at the highest level of Old Trafford about Mourinho’s managerial style and specifically the elements of his work that led them to decide against employing him when Sir Alex Ferguson retired in 2013.