The 54-year-old won LaLiga, the Copa del Rey and the Supercopa de Espana during a three-year spell at the Santiago Bernabeu before he returned to England to take charge of Chelsea for the second time.
Madrid scored a league-best 121 goals in their title-winning campaign of 2011-12, while they also won a record 16 away matches and 32 in total - a figure that was matched by Barcelona a year later.
United have shown progress since Mourinho replaced Louis van Gaal as manager but have often been found wanting in front of goal this season, failing to score in home games against Burnley and Bournemouth and only finding the net more than three times in a single match on one occasion.
Mourinho claims he would be "in s***" if he used a counter-attacking style at Old Trafford but admits that United are limited given their lack of pace.
Asked if he does not like possession-based play, he told France Football: "That is not true. This season, we have an enormous percentage of ball possession in almost all our matches. But again, everything depends on the technical characteristics of the players that you have at your disposal. On what will enable the team to win.
"People sometimes confuse ball possession with the number of goals you score. They forget that the aim is to always score and win. At Real, I had a team that broke the record for the number of goals scored in the history of the Spanish league: 121 goals in one season. It was the best in the world in terms of transition play, in terms of being effective in recovery, and then in terms of projecting the ball towards the goal.
"Cristiano Ronaldo was 27, [Angel] Di Maria was 23, [Karim] Benzema and [Gonzalo] Higuain were 23 or 24. It was the team that killed everyone. Why would I change that? Because the Manchester United team is different. It is slower. They do not have quick players and have a desire to have the ball, in order to be dominant with play.
"Zlatan Ibrahimovic needs touches of the ball in order to play. [Ander] Herrera, [Michael] Carrick and [Paul] Pogba, too. Sometimes, in the last 20 minutes, I explore other options, and I put Marcus Rashford on to go in another direction. But, generally, I try to make do with the qualities that my players have.
"My team plays in this way or that way because that corresponds to the players that I have. It is as simple as that. If I tried to play on the counter with Manchester United, I am in s**t. If you want to play possession with a team where the players dribble a lot, take the maximum risks, push forward quickly, I would kill the potential of the players.
"I could have said to Di Maria, who was faster than an arrow: 'You do not dribble, you play with one touch, you pass the ball, because I do not want to lose'. But I prefer to play with the qualities that my players have."
8 - Jose Mourinho has won each of his last 8 European home games (Chelsea – 3, Man Utd – 5), scoring 21 and conceding just 2. Powerhouse. pic.twitter.com/Nfaonqxc25— OptaJoe (@OptaJoe) March 16, 2017
Mourinho was appointed to replace Van Gaal, whose cautious approach had caused huge frustration among United fans despite delivering the FA Cup for the first time since 2004.
However, the former Inter boss says he learned a valuable lesson from his predecessor during their time at Barcelona that he still utilises to this day.
"I do not need 'yes men'," he said. "I want people who have their own opinions. And even people who contest my decisions, questioning them.
"I always say to my assistants: 'During the match, I want to think alone'. I do not want to have someone who is going to talk next to me, to tell me things. In those moments, I want to put together my expertise, with my instinct, with my feeling.
"I want to manage the team by myself. During the week, however, before or after matches, I am counting on them to behave like managers, who think for themselves, who think about what I say, who criticise me, who ask me questions for me to explain what I am doing with the team. I learnt that at Barcelona with Mr Van Gaal. That is what he demanded from his assistants."