Arsenal slayers Fleetwood Town will be up against the winners of Everton vs Newcastle United, who meet on Thursday night.
Rounding off the quarter-final lineup, Sunderland will visit 2025 FA Cup winners Crystal Palace.
Man City progressed after beating Brighton on penalties. Their reward is a clash against League One Bradford at the Etihad as they aim to defend their crown.
Liverpool set up a last-eight meeting with Bournemouth, the former club of manager Andoni Iraola, after overcoming Chelsea at Anfield in a shootout.
Sunderland, who have had little to celebrate domestically this season, booked their spot with a win over Brentford and will now face a Palace side seeking another cup run.
The quarter-final ties are to be played in the week commencing 14th December.
Full draw
Fleetwood vs Everton or Newcastle
Manchester City vs Bradford City