Chelsea visit Leicester while Arsenal face the tricky trip to Sheffield United in the quarter-finals of the FA Cup.
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.
FA CUP QUARTER-FINAL DRAW
Sheffield United v Arsenal
Newcastle v Manchester City
Norwich v Derby or Manchester United
Leicester v Chelsea
The Gunners overcame League One outfit Portsmouth 2-0 on Monday while the Blades needed extra time to beat Championship side Reading on Tuesday.