Pep Guardiola's side beat Liverpool conquerors Plymouth 3-1 on Saturday and the competition remains the last realistic hope of silverware in an otherwise difficult campaign at home and in Europe.
Manchester City lost 2-1 in their trip to Bournemouth earlier in the season and the Cherries sit just four points behind the reigning English champions in the Premier League.
After beating Manchester United on penalties at Old Trafford minutes before the draw, Fulham were handed a home tie against Premier League rivals Crystal Palace.
Preston's reward for a fairytale FA Cup run is a visit from Champions League high fliers Aston Villa, who will fancy their chances at lifting the country's biggest domestic trophy for the first time since 1957.
Brighton will play Nottingham Forest or Ipswich having knocked out Newcastle on Sunday.
The quarter-final matches will take place across the weekend of Saturday, March 29th.
FA Cup quarter-final draw in full:
Fulham v Crystal Palace
Preston v Aston Villa
Bournemouth v Manchester City
Brighton v Nottingham Forest or Ipswich