BBC Radio 5 Live’s Monday Night Club will have live coverage of the ceremony from 8.45pm.
Former City defender Micah Richards will be joined by Rachel Brown-Finnis to conduct the draw, with Mark Chapman hosting.
The last-eight ties are scheduled for Sunday, 15 March, with the final at Wembley on 9 May.
City made it through to the quarter-finals with a 10-0 win over Ipswich Town on Sunday afternoon.
Quarter-final draw numbers
1. Bristol City or Everton
2. Coventry United or Tottenham Hotspur
3. Leicester City or Reading
4. Crystal Palace or Brighton
5. Manchester City
6. Arsenal or Lewes
7. Birmingham City
8. Chelsea or Liverpool