Holders Arsenal have been drawn against Championship side Middlesbrough in the fifth round of the FA Cup.
Aitor Karanka's side knocked out Manchester City in the fourth round and will visit Emirates Stadium on Sunday, 15 February.
League One side Bradford City are rewarded for eliminating Chelsea with a home tie against Sunderland.
Another League One side, Preston North End will face Manchester United on Monday, 16 February live on BBC1.
|FA Cup fifth-round draw|
|Crystal Palace v Liverpool||Arsenal v Middlesbrough|
|Aston Villa v Leicester City||West Brom v West Ham|
|Bradford City v Sunderland||Blackburn Rovers v Stoke City|
|Derby County v Reading||Preston North End v Manchester Utd|
Crystal Palace will host Liverpool while there are all-Premier League ties between Aston Villa and Leicester City, and West Brom and West Ham.
After beating Rochdale, Stoke will visit Championship side Blackburn Rovers in the next round.
The final tie is an all-Championship affair between Derby County and Reading.
Reflecting on the draw, Match of the Day presenter Gary Lineker, who drew the balls on The One Show along with the programme's co-presenter Alex Jones, said: "You would expect Manchester United ought to go through from their replay and then a game against a League One side would be a classic FA Cup tie."
"Bradford might have wanted something a little bit more exciting than Sunderland but they'll think they have half a chance and could go on to bigger and better things."
Bradford defender Andrew Davies told BBC Radio 5 live: "It's a fantastic draw. It's good to have a home game and the fans will be right behind us. It's exciting. I can't see why we can't get another win."