Danny Wilson’s League One high-fliers will travel to face Reading.
There is potential for a Yorkshire derby if Hull City can overcome Leyton Orient in the second round with Barnsley lying in wait.
Leeds United have the plum tie of Tottenham at home, if they can win at Birmingham City in their third-round replay.
Sheffield Wednesday must beat MK Dons in their replay to book a visit to a Premier League ground, either QPR or West Brom.
Huddersfield Town face Championship rivals Leicester, who beat them 6-1 in the league on New Year’s Day.
FA Cup fourth round draw
Norwich v Luton
Oldham v Mansfield or Liverpool
Macclesfield v Wigan or Bournemouth
Derby v Blackburn
Hull or Leyton Orient v Barnsley
Middlesbrough v Aldershot
Millwall v Aston Villa
Leeds or Birmingham v Tottenham
Brighton v Swansea or Arsenal
Crystal Palace or Stoke v Manchester City
West Ham or Manchester United v Fulham or Blackpool
Southend or Brentford v Chelsea
Reading v Sheffield United
Huddersfield v Leicester
QPR or West Brom v Sheffield Wednesday or MK Dons
Bolton or Sunderland v Cheltenham or Everton
Ties to be played on the weekend of January 26-27.