The Blues moved through to the last eight with a 2-0 win over Fulham at the Etihad Stadium, thanks to two goals from Brahim Diaz.
The game will be played on the week commencing 17 December, with the exact time and date to follow.
Sky will also be selecting matches for live coverage.
Due to the tragic events at the King Power Stadium on Saturday evening, Leicester City’s Round Four Carabao Cup tie with Southampton, scheduled for Tuesday 30 October, was postponed. The game will now take place on Tuesday 27 November.
City, the current holders, are looking to win the competition for the sixth time in the Club’s history.
Full quarter-final draw:
Arsenal v Tottenham
Leicester or Southampton v CITY
Middlesbrough v Burton
Chelsea v Bournemouth