The Blues will travel to face either Crystal Palace or Bolton Wanderers in the last 32 with a replay to decide who faces the Blues.
Sam Allardyce is the new boss at Selhurst Park and City have already beaten Palace earlier this season with Yaya Toure's brace securing a 2-1 win over the Eagles in November.
While Big Sam's side will be favourites to win the replay, Phil Parkinson's Bolton will be buoyed by the prospect of a full-house and a Greater Manchester derby if they win through.
City have met Palace three times in the FA Cup, losing the first tie 2-0 in 1921 but then recording a whopping 11-4 win over the Eagles.
The last time the teams met in this competition was in 1981 on the way the the Centenary FA Cup final when the Blues triumphed 4-0.
If City do face Palace, it will be the 18th time in succession the Blues have faced opposition from the Premier League or Championship.
City and Bolton share a rich FA Cup history having met nine times including the 1904 FA Cup final that the Blues won 1-0 -coincidentally played at 'The Crystal Palace' and the 1926 FA Cup final that Wanderers edged 1-0.
The Blues have won five times, drawn one and lost three of the nine meetings.
Despite the numerous clashes, it is 70 years since the last FA Cup meeting.
The fourth round matches will take place on the weekend of January 28/29.
Draw in full:
Tottenham Hotspur v Wycombe Wanderers
Derby County v Leicester City
Oxford United v Newcastle United or Birmingham City
AFC Wimbledon or Sutton United v Cambridge United or Leeds United
Plymouth Argyle or Liverpool v Wolverhampton Wanderers
Southampton or Norwich City v Arsenal
Lincoln or Ipswich v Brighton
Chelsea v Brentford
Manchester United v Wigan Athletic
Millwall v Watford
Rochdale v Huddersfield Town
Burnley or Sunderland v Fleetwood Town or Bristol City
Blackburn Rovers v Barnsley or Blackpool
Fulham v Hull City
Middlesbrough v Accrington Stanley
Crystal Palace or Bolton v Manchester City