The ties are set to be played week commencing December 19 - just after the World Cup final in Qatar.
With the Premier League not set to resume until Boxing Day, it remains to be seen which top-flight players will be involved in the domestic cup competition.
Carabao Cup holders Liverpool edged past Sky Bet League One Derby after a penalty shootout, while City beat Chelsea, last season's Carabao Cup runners-up.
The two sides also met ahead of the new campaign in the FA Community Shield, with Liverpool running out 3-1 winners.
Manchester United booked their place in the last 16 with a 4-2 win over Aston Villa on Thursday night and will again be at home in the next round against current Championship leaders Burnley.
League Two Gillingham pulled off a shock penalty shootout win at Brentford, and have been rewarded with a trip to Wolves.
Championship promotion hopefuls Blackburn beat West Ham 10-9 on spot-kicks and will be at home against Nottingham Forest, who put Tottenham out on Wednesday night.
Brighton won 3-1 at Arsenal and have been handed another trip to London, away at Charlton.
New Southampton boss Nathan Jones will be hoping to avoid an upset in their home tie with League One Lincoln, who knocked out Bristol City in round three.
In an all-Premier League tie, Newcastle will host Bournemouth, who were 4-1 winners over Everton, while Leicester travel to MK Dons.