The last-16 first leg match represents the first time the clubs have met in almost a decade and Mourinho said on Tuesday it was the kind of challenge he and his players relished.
"We all want to play against big opponents, big coaches, big players, big teams and United represent all of that," Mourinho told a news conference at Real's Bernabeu stadium. "I think it's easier for the players.
"One of the things we have missed this season is the appetite and motivation to play against smaller opponents and because of that we lost so many points in the Spanish league against teams we would normally beat.
"This is a little bit the history of this team. If history means something tomorrow we have the biggest opponent and we should have a good answer," said the former Chelsea coach who renews his rivalry with United counterpart Sir Alex Ferguson.
The Champions League is the overwhelming priority for Real this term as their hopes of a second straight La Liga title have all-but disappeared after shock defeats to the likes of Granada and Getafe.
By contrast, Mourinho's men beat Barcelona over two legs to win the Spanish Super Cup and held their arch rivals to a 2-2 draw at the Nou Camp in a league game in October.
Mourinho has faced United twice before at this stage of the Champions League, starting with his old club Porto's success on the way to winning the trophy in 2004.
As Inter Milan coach, the Portuguese lost to United in the last-16 five years later but during three years at Chelsea he suffered only one reverse to the Manchester club in all competitions, winning five games and drawing four.
Mourinho, who reiterated his desire to return to England when his stint at Real ends, would not be drawn on his tactical plans for Wednesday's game.
"I think they [United] also want to know what you want to know," he said. "We did tactical work today but you will have to ask your sources about it because I am not going to give anything away.
"We don't know if we will be successful but we are perfectly clear about what we want to do. For sure it's the most important match of this round of the Champions League," added Mourinho.
"This press room completely full is representative of what this match means to the world of football. Sometimes the expectation is high and the quality of the match is not so good but I hope the world gets what they want."
