After beating Port Vale 4-1 at the Etihad Stadium on Monday (AEDT), City was pitted against Fulham – 2-1 victor against Premier League side Aston Villa – in the draw for the fourth round.
A youthful Liverpool side beat Merseyside rival Everton 1-0 to progress and its reward will be a clash with whoever wins the replay between Bristol City and Shrewsbury.
If Manchester United gets past Wolves at the second attempt, it faces a trip to Watford or Tranmere Rovers.
Chelsea was given a trip to Hull City, while Tottenham must go to Southampton if it emerges from its replay with Middlesbrough triumphant.
Arsenal will head south to Bournemouth after its 1-0 win over Leeds United.
FA Cup fourth round draw in full:
Watford or Tranmere Rovers v Wolves or Manchester United
Hull City v Chelsea
Southampton v Middlesbrough or Tottenham
QPR v Sheffield Wednesday
Bournemouth v Arsenal
Northampton Town v Derby County
Brentford v Leicester City
Millwall v Sheffield United
Reading or Blackpool v Cardiff City or Carlisle United
West Ham v West Brom
Burnley v Norwich City
Bristol Rovers or Coventry City v Birmingham City
Manchester City v Fulham
Rochdale or Newcastle United v Oxford United
Portsmouth v Barnsley
Bristol City or Shrewsbury Town v Liverpool