Manchester City will go to Championship side Bristol City in the FA Cup fifth round.
Five of the eight ties are subject to a replay, including the winner of non-league Wrexham and Sheffield United landing a home meeting with Tottenham.
Manchester United will host West Ham after they beat League One Derby County 2-0 on Monday night.
If Luton Town beat Grimsby Town they will face their former manager Nathan Jones' Southampton.
At least one English Football League team will be in the quarter-finals with Ipswich Town or Burnley drawn at home to Sheffield Wednesday or Fleetwood Town.
The games will take place on the week of Wednesday, 1 March.
FA Cup fifth round draw in full:
Southampton v Luton Town or Grimsby Town
Leicester City v Blackburn Rovers or Birmingham City
Stoke City v Brighton & Hove Albion
Wrexham or Sheffield United v Tottenham Hotspur
Fulham or Sunderland v Leeds United
Bristol City v Manchester City
Manchester United v West Ham United
Ipswich Town or Burnley v Sheffield Wednesday or Fleetwood Town