Ferguson himself said recently the former Chelsea boss "could manage anywhere", a statement taken by many as backing for Mourinho as a future United manager.
But the Portuguese is not so popular in all corners of the club.
Charlton, a director and ambassador at United, has been unimpressed by some of Mourinho's antics, such as his outspokenness and his attack on Tito Vilanova, then the assistant manager at Barcelona.
"A United manager wouldn't do that," Charlton said in The Guardian. "Mourinho is a really good coach but that's as far as I would go really. He's the manager of Real Madrid and we expect to play them in the Champions League by the end of the season."
When it was suggested a United manager would not get away with such behaviour, he added: "You are right. He pontificates too much for my liking. He's a good manager, though."