Los Blancos are in the midst of a disappointing La Liga campaign and currently sit third, with a seemingly unattainable gap of 18 points separating them from Barcelona.
Mourinho was in Manchester on Sunday to watch United against Liverpool ahead of their meeting on February 13, and was keen to point out the magnitude of such a tie.
"This is the match the world wants to see," he told The Sun.
|6/4||Manchester United are 6/4 with Bet365 to progress to the Champions League quarter-finals|
"We know we can beat them. We know they can beat us — but we will be ready."
Sir Alex Ferguson is hoping to win his third Champions League with United, while Mourinho is bidding to become the first manager to win the competition with three different clubs, and says their tough group stage has prepared them well.
"There were groups where you knew who was going to be first and second after two or three games," added Mourinho.
"But our group included three of the best five teams in the competition — Borussia Dortmund, Manchester City and ourselves.
"Now we get the toughest opponent in the biggest tie of the last 16."