FA Cup holders Liverpool will face another Premier League opponent in the fourth round - if they get past Wolves.
Brighton will host the winner of their replay.
Paul Ince returns to Manchester United as Reading manager, while Tottenham have a potentially difficult tie at Preston.
Either Chelsea or Manchester City will play Oxford or Arsenal at home.
Leeds - who drew with Cardiff this afternoon - could end up taking on Boreham Wood or Accrington Stanley.
Among the other fixtures, Southampton host Blackpool, West Ham travel to Derby, Leicester are at Walsall and Fulham welcome Sunderland.
FA Cup fourth round draw:
Preston v Tottenham
Southampton v Blackpool
Wrexham v Sheffield United
Ipswich v Burnley
Manchester United v Reading
Luton or Wigan v Grimsby
Derby v West Ham
Stoke v Aston Villa or Stevenage
Blackburn v Forest Green or Birmingham
Walsall v Leicester
Sheffield Wednesday v Fleetwood
Manchester City or Chelsea v Oxford or Arsenal
Bristol City or Swansea v Chesterfield or West Brom
Brighton v Liverpool or Wolves
Fulham v Sunderland
Boreham Wood or Accrington Stanley v Cardiff or Leeds
Ties to be played between 27th to 30th of January.
