Winners of the competition in four of the last five seasons, Manchester City, defeated defending champions Liverpool 3-2 in an entertaining game at the Etihad Stadium on Thursday and the reward for Pep Guardiola's side will be a trip to fellow Premier League side Southampton.
Southampton defeated League One side Lincoln City 2-1 on Tuesday.
After seeing off Vincent Kompany's high flying Burnley side at Old Trafford on Wednesday, Manchester United get another home game against League One opposition Charlton Athletic, who knocked out Brighton and Hove Albion on penalties.
Newcastle United will lock horns with Leicester City for a place in the semi-finals after seeing off Bournemouth and MK Dons respectively.
Nottingham Forest will square off with Wolverhampton Wanderers in the last eight.
The quarter-finals will take place in the week commencing 9 January.
Full quarter-final draw:
Manchester United v Charlton Athletic
Southampton v Manchester City
Nottingham Forest v Wolves
Newcastle United v Leicester City
