Gareth Taylor’s side will play the first leg in Monza, Italy on 24 March at 11.30am UK time, before hosting the Primera División outfit at the Academy Stadium in the reverse fixture on 31 March at 4pm UK time.
Should City progress, we will face either Paris Saint-Germain, Sparta Prague or Olympique Lyonnais in the semi-finals on 24/25 April and 1/2 May, with the first leg away from home.
Semi-finalists in 2017 and 2018, City reached the last eight stage with comprehensive victories over Göteborg FC and Fiorentina.
Barcelona were runners-up in 2019 and have faced City once before: in a pre-season friendly in 2018. City triumphed 2-0, thanks to goals from Melissa Lawley and Nikita Parris.
We have met Lyon twice before in the Champions League (as well as twice in pre-season fixtures) and were edged out by the reigning Champions on both occasions, while we have only met two-time runners-up Paris Saint-Germain in pre-season and have never played Sparta Prague.
Lyon are aiming to extend their record of five titles in a row and seven overall.
Sparta Prague and Paris Saint-Germain are yet to meet in the Round of 16 second leg, which takes place on Wednesday 17 March.
Fixture information will be confirmed in due course...
Full Quarter-final draw
Bayern Munich v FC Rosengard
Sparta Prague / Paris Saint-Germain v Olympique Lyonnais
FC Barcelona v Manchester City
Chelsea v Wolfsburg
Full semi-final draw
Sparta Prague / Paris Saint-Germain / Olympique Lyonnais v Barcelona / City
Bayern Munich / Rosengard v Chelsea / Wolfsburg
Quarter-finals: 24/25 March & 31 March/1 April
Semi-finals: 24/25 April & 1/2 May
Final: 16 May (Gamla Ullevi, Gothenburg)