The Portuguese coach had been under pressure throughout the campaign amid United's disappointing results and his issues with some of his star players.
However, there were reports that a route back to Madrid could open up as president Florentino Perez was interested in working with him again.
When asked if he would like to see his former coach return to the Santiago Bernabeu, the Brazilian full-back would not go much further than expressing his sympathy.
"[His sacking] is a pity as he is a great coach and for him to be without a club is a pity," he told reporters. "It's not for me to say if he should come to Real Madrid, but I really appreciate all he did for me at this club.”
Madrid have had to overcome their own coaching troubles this season. After sacking Julen Lopetegui just a few weeks into his spell in charge, they recently handed Santiago Solari a contract that runs until 2021.
However, the new boss was asked if he worries Mourinho could be brought in to replace him in the wake of his sacking.
"How would I be worried about rumours or speculation about Real Madrid?" he replied. "It happens every day, it is just part of our reality.
"I feel the same as when I arrived here to work as a coach, and further back as a player. That is to give everything in my job every day, that is my way of viewing football.”
Madrid are in the United Arab Emirates to compete in the FIFA Club World Cup and will take on Kashima Antlers in the semi-final.