Manchester United will host Liverpool in the FA Cup fourth round following the draw on Monday, with a home tie also awaiting in round five.
Current holders Arsenal will head to either Southampton or Shrewsbury, while Tottenham have been handed a trip to Wycombe.
Chelsea have been given a home tie against Luton, while Manchester City head to Cheltenham.
The fifth round sees United or Liverpool then play host to the winner of the Stockport/West Ham v Doncaster ties.
FA Cup 4th-round draw in full:
Cheltenham Town v Manchester City
Bournemouth v Crawley Town
Swansea v Nottingham Forest
Manchester United v Liverpool
Southampton/Shrewsbury v Arsenal
Barnsley v Norwich
Chorley v Wolves
Millwall v Bristol City
Brighton v Blackpool
Wycombe v Tottenham
Fulham v Burnley
Sheffield United v Plymouth
Chelsea v Luton
Stockport/West Ham v Doncaster
Brentford v Leicester
Everton v Sheffield Wednesday
Ties to be played January 22-25
FA Cup 5th-round draw in full:
Fulham/Burnley v Bournemouth/Crawley
Manchester United/Liverpool v Stockport/West Ham or Doncaster
Sheffield United/Plymouth v Millwall/Bristol City
Chorley/Wolves v Southampton/Shrewsbury or Arsenal
Barnsley/Norwich v Chelsea/Luton
Everton/Sheffield Wednesday v Wycombe/Tottenham
Swansea/Nottingham Forest v Cheltenham/Manchester City
Brentford/Leicester v Brighton/Blackpool
Ties to be played February 9-11