The 28-year-old has so far refused to sign a new contract with the Spanish giants, with his current deal set to expire in the summer of 2015.
Red Devils boss Sir Alex Ferguson has been heavily linked with a move for the Portuguese forward, who left Old Trafford in a club-record £80million transfer in 2009.
Manchester United are believed to be weighing up a cut-price £55million bid, with club sponsors Chevrolet and Nike helping to pay for the Real Madrid star's extravagant wage demands.
Ronaldo revealed he was unhappy in the Spanish capital earlier in the season, but Mourinho has since advised the 2013 Ballon d'Or runner-up that "it would be good" if he decided to stay put.
"When you have a player with these characteristics, you have to do all that is possible not to lose him," said the Real Madrid boss. "It would be fantastic for the club and vital [if he stayed].
"It's obvious that he can play wherever he wants to play. [But] it would be good for Real Madrid as well as Ronaldo if he continued."
There are question marks still hanging over Mourinho's own future, with the Portuguese tactician odds-on favourite to make an emotional return to Chelsea in the summer.
After reported fall-outs with the Real Madrid hierarchy, the 50-year-old's chances of managing in La Liga next season are anything but certain, and the outcome will likely have a significant impact on Ronaldo's decision to stay or go, given their close relationship.