The Red Devils should replace Louis van Gaal with the former Chelsea manager this summer, according to the ex-Blackburn Rovers striker
Mourinho, without a job since leaving Chelsea, has been heavily linked with the post at Old Trafford with United struggling under Van Gaal this season.
And McCarthy, a United fan who won the Champions League under the Portuguese tactician at Porto in 2003-04, said the Premier League giants should chase the 53-year-old.
“I think we need somebody that will steer the ship with immediate results but also as a long-term successor,” the former Blackburn striker told Omnisport.
“The good old days of Sir Alex Ferguson are long gone.
“I think we have to try and captivate those moments back and for me the only example I can give for someone who can get United back on that path is Jose.”
McCarthy said Mourinho had already proven he could turn teams around, having led Chelsea to three league titles and multiple cups.
“He turned Chelsea into one of the biggest teams in Europe; he made them one of the most feared teams to play [against] and into a powerhouse and a European household name,” he said.
“He has come to an average English team, a big name, but an average team at the time, and has turned them into world beaters.”
United’s rivals Manchester City have already made a move, appointing Pep Guardiola ahead of next season.
McCarthy believes Mourinho is as good as the Bayern Munich coach, with whom he shared a rivalry during their time in La Liga.
“Mourinho’s tactics and ability matches Pep Guardiola,” he said.
“I think of the arrogance and there is enough testosterone there not to fear anything that Man City will throw at Man United next season if he goes.”