Draw hands Lee Johnson's side a potential away draw.
City know a trip to Premier League opponents awaits in the Emirates FA Cup fourth round - if they can overcome Fleetwood Town in next week's replay.
Lee Johnson's men face a trip to either Burnley or Sunderland - who drew 0-0 at the Stadium of Light on Saturday - if they win at Highbury Stadium on January 17th.
Sunderland, managed by David Moyes, are currently 18th in the Premier League, while Burnley - with Tom Heaton and Sam Vokes in their ranks and Sean Dyche in charge - are up in 12th.
Head coach Lee Johnson said: "We still have a job to do against Fleetwood and the replay at their place is going to be a very tough proposition indeed. Make no mistake, we cannot afford to take them lightly or look too far ahead."
If City progress in the replay, the fourth round tie would take place over the weekend of January 27-30, forcing a postponement of the league match at Aston Villa.
Fourth round 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 Wolves
Southampton or Norwich City v Arsenal
Lincoln City or Ipswich Town v Brighton & Hove Albion
Chelsea v Brentford
Manchester United v Wigan Athletic
Millwall v Watford
Rochdale v Huddersfield Town
Burnley or Sunderland v Bristol City or Fleetwood Town
Blackburn Rovers v Barnsley or Blackpool
Fulham v Hull City
Middlesbrough v Accrington Stanley
Crystal Palace or Bolton Wanderers v Manchester City