In the other ties Manchester United will host Fulham, while League Two‘s Grimsby Town will travel to face Premier League Brighton and Sheffield United and Blackburn Rovers will face off in an all-Championship battle.
Kompany won four Premier League titles and two FA Cups during his 11-year stay at Man City before leaving to begin his coaching career in 2019. He has led Burnley to the top of the Championship table this season.
Grimsby produced the shock of the fifth round when knocking out Premier League Southampton 2-1 on Wednesday to earn the fourth-tier side a first FA cup quarterfinal appearance in 84 years.
Sheffield United caused their own upset when beating Tottenham 1-0, meaning four of the traditional top six — also including holders Liverpool, Arsenal and Chelsea — have already been eliminated from the competition.
With Sheffield United and Blackburn drawn against each other, it means there is guaranteed to be at least one non-Premier League side in the semifinals.
Matches will take place between March 17-19.
Full FA Cup quarterfinal draw:
Manchester City vs. Burnley
Manchester United vs. Fulham
Brighton vs. Grimsby
Sheffield United vs. Blackburn