Non-league Chorley will host Premier League Wolverhampton Wanderers after beating a depleted Derby County in the third round.
League Two Cheltenham Town are set to welcome Pep Guardiola’s Manchester City to Whaddon Road.
The fourth-round ties will be played the weekend of 23-24 January.
Crawley Town, who celebrated a famous 3-0 win over Leeds United on Sunday, will travel to Championship side Bournemouth in the next round.
Jose Mourinho’s Tottenham will face Wycombe Wanderers at Adams Park, while Fulham take on Burnley in an all-Premier League tie.
Chorley would face 14-time winners Arsenal in the fifth round – if the National League North side overcome Wolves and the Gunners beat either Southampton or Shrewsbury.
David Moyes could return to former club Manchester United in the last 16 if West Ham beat League One Doncaster Rovers and United seal victory over Liverpool in the fourth round.
The fifth-round ties will be played 9-11 February.