Mourinho welcomes United to the Spanish capital in the first leg of their last-16 clash in the Champions League on Wednesday with words of praise for the English club.
"It is always a privilege, not just when you win, we all want to play against big opponents, big coaches, and big teams and Manchester United represents all of that," he told reporters.
"I remember every match, every result against them. Tomorrow is one more and I hope the Old Trafford second leg in three weeks time is not the last."
Mourinho is widely expected to take over at United when Sir Alex Ferguson retires.