The pair have clashed in the Premier League and Champions League over the years and Mourinho is looking forward to again doing battle with the Scottish great in the Round of 16 first leg at the Santiago Bernabeu on Wednesday.
"I feel privileged about that because he is such an important person in the world of football and, more importantly than that, he is good person," said Mourinho.
"I have always had a fantastic relationship 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. At all of my clubs I have met Manchester United and Sir Alex.
"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 I want to win.
"I had some boys who played 90 minutes last Wednesday for their national teams and I could give them a rest, but it is such a big match on Wednesday that everyone wants to play, no one will be tired."