Carvalho, who currently plays for Monaco in Ligue 1, won trophies under Mourinho at Porto, Chelsea and Real Madrid.
And the 38-year-old has backed Mourinho to lead United to their first title since Sir Alex Ferguson retired in 2013.
"Jose will have something to prove after what happened at Chelsea," Carvalho said in quotes reported by the Sun.
"I think he will make Manchester United better and in the next two years they will be champions
"United have struggled since Ferguson retired but Jose can be the one to replace him.
"He is a great coach and now he is in a great club - United are one of the biggest in the world.
"I have no doubt that he can bring trophies back to United again and that he will make them champions.
"I don't know if it will be in the first year, the second year or the third, but Mourinho will win the title again
My prediction is that it will be in the second year."
Source : PA
Source: PA