"But once we play to our capabilities, we can give every team in the world a good game.
The first leg will be played on 4-5 April, with the second leg on 18-19 April.
In the other quarter-finals, Spain's Valencia will play Lazio of Italy, who triumphed 2-1 over Chelsea at Stamford Bridge on Wednesday to top their group.
Form team Bayern Munich of Germany and Porto complete the last eight draw in a re-run of the 1987 final, which the Portuguese side won 2-1.
Sir Alex Ferguson's team will be looking forward to getting stuck into Real Madrid, who have underperformed in domestic competition this season.
But Dwight Yorke said that the Spanish side still had enough quality to be a threat.
"If they play to their capabilities, then they can give anybody a game," he said.
"But once we play to our capabilities, we can give every team in the world a good game.
"They won't want to see us at our best, because we can be very dangerous."
Real, who boast the talents of England's Steve McManaman, won the Champions League in 1998 and ended Manchester's first run in the competition back in 1957.
Meanwhile, Chelsea managing director Colin Hutchinson tipped his side as the underdogs.
"But we are looking forward to it immensely," he said.
"We have a hell of a lot to play for over the last two months of the
season."
In addition to European commitments, Chelsea have an FA Cup semi-final with Newcastle and a place in next year's Champions League to chase through the Premiership.
The draw for the semi-final was also held and it keeps alive the possibility of holders Manchester United meeting their Premiership rivals in the final, or an all-Spanish final if the two English teams should slip up.
Manchester would have to overcome Bayern Munich or Porto in the semis to reach their second consecutive final, while Chelsea could face a rematch with Lazio or dangerous Spaniards Valencia.
The legs of the semis will be held on 2-3 May and 9-10 May, with the final in Paris on 24 May.