The two teams will face off at Old Trafford on the weekend of Jan. 23.
Holders Arsenal will go to Southampton, if they win their third-round match at Shrewsbury, while Manchester City travel to Cheltenham.
The draw for the fifth round was also held Monday, to avoid fixture congestion.
Winners of the Manchester United-Liverpool match will have a home tie against either Doncaster Rovers or West Ham.
Fourth-round draw: (matches to be played weekend of Jan. 23):
Cheltenham Town vs Manchester City
Bournemouth vs Crawley Town
Swansea City vs Nottingham Forest
Manchester United vs Liverpool
Southampton or Shrewsbury Town vs Arsenal
Barnsley vs Norwich City
Chorley vs Wolverhampton Wanderers
Millwall vs Bristol City
Brighton & Hove Albion vs Blackpool
Wycombe Wanderers vs Tottenham Hotspur
Fulham vs Burnley
Sheffield United vs Plymouth Argyle
Chelsea vs Luton Town
West Ham United vs Doncaster Rovers
Brentford vs Leicester City
Everton vs Sheffield Wednesday
Fifth-round draw: (matches to be played weekend of Feb. 10)
Manchester United or Liverpool vs West Ham or Doncaster Rovers
Sheffield United or Plymouth Argyle vs Millwall or Bristol City
Chorley or Wolves vs Southampton or Shrewsbury Town or Arsenal
Barnsley or Norwich City vs Chelsea or Luton Town
Everton or Sheffield Wednesday vs Wycombe Wanderers or Tottenham Hotspur
Swansea or Nottingham Forest vs Cheltenham or Manchester City
Brentford or Leicester vs Brighton or Blackpool.(dpa/NAN)