The United striker has been plunged into despair following lurid allegations in the media about his personal life, and the Madrid giants are eager to add an extra strong striker to their side.
Mourinho is a known admirer of the England international but United boss Sir Alex Ferguson will be hoping that the Portuguese does not tempt Rooney to the Santiago Bernabeu.
Mourinho had already told Ferguson to ‘rest easy’ and that Rooney’s switch to Madrid would be ‘impossible’.
However, Mourinho will definitely be keen to bolster his attacking ranks with the addition of Rooney should the former Everton ace decide it is time to quit English football and move abroad.
Real Madrid president Florentino Perez has reportedly told Mourinho that £65m will be put aside to bring Rooney to Spain.
Sources in Spain said: “A move for Rooney is not impossible.
“There were doubts that David Beckham and Cristiano Ronaldo would be allowed to join Real but both arrived at the club.”
Rooney was left out of United’s trip to Everton as Ferguson wanted to protect him from possible verbal abuse at Goodison Park.
If the situation gets worse for Rooney, he could well be set to depart from Old Trafford.
Real Madrid are sure to be waiting for a sign of disenchantment with English life to make a massive bid and lure Rooney to Santiago Bernabeu.