United head to the Bernabeu for the first leg on Wednesday, before the tie is decided at Old Trafford three weeks later. The only certainty will be one of the heavyweights getting knocked out at the end, with Cristiano Ronaldo pitted against his old club in a mouthwatering duel.
"It is the match the world is waiting for," Mourinho told MUTV.
"People think we are under pressure because a big team will be out. But it is the kind of match we want and the people are not waiting for any other game. I hope we give them what they want."
After Ronaldo bagged yet another hat-trick in Real's win over Sevilla on Saturday night, Mourinho flew into Manchester to watch United overcome Everton at Old Trafford.
And, despite the impending battle, Mourinho was welcomed into Sir Alex Ferguson's inner sanctum prior to the 2-0 win, a sign of just how much affection the pair hold for each other.
"I feel privileged about that because he is such an important person in the world of football and, more importantly, he is good person," said Mourinho.
"I have always had a fantastic relationship with him and I am proud of it.
"We have had so many matches between us which started with Porto. We had some with Chelsea, Inter and now Real. Some I had won, some I have lost, others I have drawn.
"Of course, I want to win and he wants to win, but I believe the loser will have a little bit of space to feel a little bit happy because of the friendship. But make no mistake, I want to win."