Third Division Northampton will play 10-times FA Cup winners Manchester United in the fourth round if they can beat Rotherham in a replay next week.
Conference side Scarborough could face a home clash with Premiership glamour team Chelsea if both sides overcome replays against Southend and Watford respectively.
Elsewhere there were four all-Premiership ties - the pick of them being Liverpool against Newcastle at Anfield.
Cup holders Arsenal are at home to Middlesbrough, Everton will play Fulham and Tottenham will travel to play Leicester or Manchester City.
Telford are at home to First Division Millwall in the fourth round, with ties to be played on the weekend of January 24th and 25th.
FA Cup - Fourth round draw
Manchester City or Leicester City v Tottenham Hotspur
Swansea v Preston or Reading
Northampton or Rotherham v Manchester United
Kidderminster or Wolves v West Ham
Arsenal v Middlesbrough
Coventry v Accrington Stanley or Colchester
Ipswich v Sunderland
Luton v Tranmere or Bolton Wanderers
Liverpool v Newcastle United
Burnley v Gillingham
Nottingham Forest v Sheffield United
Portsmouth v Barnsley or Scunthorpe
Everton v Fulham
Telford v Millwall
Southend or Scarborough v Watford or Chelsea
Birmingham City v Wimbledon or Stoke