Frank Lampard’s side beat Liverpool 2-0 on Tuesday night in the fifth round and will have to see off the Foxes to reach the last four.
Mikel Arteta’s Arsenal side will visit Chris Wilder’s Sheffield United after both sides progressed to the last eight.
Frank Lampard’s Chelsea side will visit Leicester in FA Cup quarter-finals after Liverpool win
The Gunners overcame League One outfit Portsmouth 2-0 on Monday while the Blades needed extra time to beat Championship side Reading on Tuesday.
Newcastle welcome FA Cup holders Manchester City while Norwich host Derby or Manchester United.
The Magpies beat Premier League promotion chasers West Brom 3-2 while City secured a 1-0 victory over Sheffield Wednesday in the fifth round.
Norwich beat Jose Mourinho’s Tottenham on penalties following a 1-1 draw on Wednesday night while United face Derby in the final fifth-round encounter on Thursday night.
The ties will be played on the weekend of March 20-22.
Newcastle will welcome FA Cup holders Manchester City in the last eight of the competition