The quarter-final ties will take place on April 5 and 6 and April 12 and 13, with the semi-finals scheduled for the end of next month and start of May.
Paris’ Stade de France will host the Champions League final on May 28.
The quarter and semi-final draw was made on Friday morning at the House of European Football in Nyon, Switzerland.
Champions League draw
Chelsea (ENG) v Real Madrid (ESP)
Manchester City (ENG) v Atletico Madrid (ESP)
Villarreal (ESP) v Bayern Munich (GER)
Benfica (POR) v Liverpool (ENG)
Chelsea are bidding to become only the second team after Real Madrid to retain the Champions League trophy and dispatched Lille in the round of 16.
Fellow Premier League clubs Liverpool and Manchester City, meanwhile, beat Inter Milan and Sporting Lisbon respectively.
Jurgen Klopp’s side reached successive Champions League finals in 2018 and 2019 – lifting the trophy in their most recent appearance – but Man City are yet to win the competition despite being the dominant force in England over the past decade, losing 1-0 to Chelsea in last season’s final.
Real Madrid, the most successful team in Champions League history, stunned Paris Saint-Germain in the last-16 round, while fellow prolific winners Bayern Munich smashed RB Salzburg 8-2 on aggregate.
Spanish champions Atletico Madrid knocked out Manchester United as they look to reach a third Champions League final under Diego Simeone and underdogs Villarreal and Benfica completed the quarter-final line-up with victories over Juventus and Ajax.