The draw took place earlier tonight on BBC Radio 5.
Rachel Brown-Finnis and Micah Richards conducted the draw, hosted by Mark Chapman.
The last-eight ties are scheduled for Sunday 15 March with the final at Wembley on 9 May.
Crystal Palace or Brighton & Hove Albion v Birmingham City
Bristol City or Everton v Chelsea
Arsenal or Lewes v Coventry United or Tottenham Hotspur
Leicester City or Reading v Manchester City
Blues qualified for the quarter-finals after a narrow 1-0 win away to Sunderland on Sunday.
Lucy Staniforth fired in a late free-kick to break the deadlock five minutes before full time to take Blues through to the last eight of the Cup.
Read the match report here.