Burnley reached the last eight of the World's oldest club competition after beating Fleetwood 1-0 on Wednesday.
The Clarets hold a virtually unassailable lead at the top of the Championship table and are primed for a swift return to the top flight after getting relegated last season.
Kompany spent eleven seasons as a player with Manchester City, winning four Premier League titles, four League Cups and two FA Cups.
Other fixtures in the quarterfinals will see Manchester United host Fulham in the only all-Premier League tie of the round.
The Red Devils defeated West Ham United 3-1 at Old Trafford on Wednesday.
Sheffield United's reward for knocking out Tottenham Hotspurs is a date with Blackburn Rovers, who stunned Leicester City 2-1 at their own backyard on Tuesday.
Brighton and Hove Albion will play at the AMEX Stadium against Grimsby Town.
The last-eight ties will be played from 17 to 19 March.
This season’s FA Cup final will be played on June 3 at Wembley.
Liverpool defeated Chelsea on penalties to win last season's FA Cup.
