There have been repeated suggestions that the Portuguese forward is seeking an exit from Real Madrid this summer, and that he could make the switch back to Old Trafford.
However, Ronaldo is reportedly reluctant to be reunited with Mourinho after the pair supposedly fell out during their final season together in the Spanish capital.
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The duo's agent, Jorge Mendes, could potentially look to smooth things over, although Ronaldo is expected to look elsewhere should he depart Real Madrid.
Mourinho last month played down rumours that Ronaldo could join United.
“I think at the moment Real Madrid is with him now. I think I should be the last one to add some fuel to the fire,” he said - as quoted by the Telegraph.
“Madrid is on fire. The results are not good, and it’s a club where I worked for three years, I care about the club and I am the last one to add fire.
“So to put some water on the fire I think Cristiano is the kind of player that every manager wants, every club wants.
“But only one manager can, only one club can have - [Zinedine] Zidane and Real Madrid, that’s my feeling.”
The relationship between the two was said to have broken down by the time of Mourinho's exit, with Ronaldo's red card in his final game - defeat in the Copa del Rey final by Atletico Madrid - the nadir.