City travel to Tottenham for the first leg on Tuesday 9 April, with the return game at the Etihad scheduled for Wednesday 17 April.
Both matches will kick-off at 8pm.
The away leg is expected to be played at Tottenham’s new stadium.
Full quarter-final draw:
Ajax v Juventus
Liverpool v Porto
Tottenham v CITY
Barcelona v Manchester United*
*United will play the first leg at home to avoid clashing with City's home fixture.
Tottenham or CITY v Ajax or Juventus
Barcelona or Manchester United v Liverpool or Porto