The draw for the FA Cup fourth round was conducted on Monday night.
Holders Manchester City have been drawn away to Tottenham Hotspur. The Premier League champions have neither scored nor won a fixture at the ground since it was opened.
The lowest-ranked side left in the competition, Maidstone United, travel to Championship high-flyers Ipswich.
Chelsea host Aston Villa and Newcastle go to Fulham are two of six potentially six all-Premier League ties.
The games will be played across the weekend of January 27.
FA Cup fourth-round draw in full
Watford vs Southampton
Blackburn vs Wrexham
Bournemouth vs Swansea
West Brom vs Brentford or Wolves
West Ham or Bristol City vs Nottingham Forest or Blackpool
Leicester vs Hull or Birmingham
Sheffield Wednesday vs Coventry
Chelsea vs Aston Villa
Ipswich vs Maidstone United
Liverpool vs Norwich or Bristol Rovers
Tottenham vs Manchester City
Leeds vs Plymouth
Crystal Palace or Everton vs Luton or Bolton
Newport or Eastleigh vs Wigan or Manchester United
Sheffield United vs Brighton
Fulham vs Newcastle