Favorite Barcelona will meet Shakhtar Donetsk, the underdog among the teams remaining in Europe's elite club competition, and defending champion Inter Milan will take on Schalke.
If Spanish rivals Barcelona and Madrid both progress, they would meet in the semifinals. They already play each other twice next month, first in the league and then in the final of the Copa del Rey.
The first legs of the quarterfinals take place on April 5-6, with the return matches a week later.
Madrid, coached by two-time Champions League winner Jose Mourinho, is through to the last eight for the first time since 2004. It will be up against a Spurs team, which finished at the top of its group, above Inter, and eliminated AC Milan in the last 16 in its first season in the competition.
“It's a tough draw but a fantastic draw,” said Tottenham manager Harry Redknapp. “It's got the makings of a great game.” Shakhtar topped its group and beat AS Roma 6-2 in the first knockout round so will not be taken lightly by Barcelona, which beat the Ukrainian team 1-0 in the 2009 UEFA Supercup — a game between the winners of the Champions League and the UEFA Cup.
“It's probably the team that has the most points and best results of the Champions League,” Barcelona coach Pep Guardiola said of Shakhtar.
“It's a very strong team with experienced players. It was very difficult for us to take the Supercup from them. We will have to play both games well.” Barcelona has lost just once in the Champions League and once in the Spanish league this season, making Pep Guardiola's side the favorite for the trophy.
“We've got the most difficult opponent,” Shakhtar captain Dario Srna said. “It will be rather difficult to advance but we will play to the last minute, to the very last second. We will try to produce a big surprise.” Chelsea's pairing with United means England's two most successful clubs in recent years will play three times in the space of a month, as they also meet in the Premier League on May 7.
United beat Chelsea on penalties in the 2008 final in Moscow to become European champions for the third time.
Inter will play a German team for the second straight round, having beaten Bayern Munich in the last 16 in a repeat of the 2010 final in Madrid.
The Italian champions, who are looking to become the first club to successfully defend the Champions League in its current format, lost to Schalke on penalties in the final of the 1997 UEFA Cup — a competition now called the Europa League.
“Getting the Champions League winner is a tough draw but maybe it's a good omen that we were already victorious (against Inter) in 1997,” said Schalke goalkeeper Manuel Neuer, whose team beat Valencia in the last 16.
“It could be an advantage that the first leg is away, but we know what happened to Bayern.” Felix Magath guided Schalke to the quarterfinals but was replaced as coach this week by Ralf Rangnick, with the team languishing in midtable in the Bundesliga.
