Manchester City were handed a tough trip to Bournemouth in Sunday's FA Cup quarter-final draw, while Aston Villa travel to second-tier Preston.
Fulham's reward for beating holders Manchester United on penalties is a home tie in a London derby against Crystal Palace.
Brighton beat Newcastle 2-1 after extra time on Sunday and will face the winners of Monday's tie between Nottingham Forest and Ipswich.
The FA Cup is City's only realistic chance of winning a trophy in what has been a difficult season for Pep Guardiola's men.
City are favourites for the competition with the Premier League's top two Liverpool and Arsenal already eliminated.
However, they lost 2-1 in their trip to Bournemouth earlier in the season and the Cherries sit just four points behind the English champions in the Premier League.
Quarter-final draw in full:
Fulham v Crystal Palace
Preston v Aston Villa
Bournemouth v Manchester City
Brighton v Nottingham Forest or Ipswich
Ties to be played on the weekend of March 29 and 30.