City face the Reds at the Academy Stadium next month and Nick Cushing’s side have already beaten the Merseysiders 3-0 in the league this season.
The teams will meet in the league again a fortnight after this tie.
The Blues last won the competition in 2017 with a 4-1 win over Birmingham City at Wembley.
This is the 49th year of the FA Women’s Cup and City are chasing silverware on three fronts with the FA Women’s Super League and Continental Cup.
READ: When is the FA Cup sixth round draw?
City progressed to the last eight with a 3-0 win over Spurs at the weekend.
Full draw:
The #SSEWomensFACup quarter-final fixtures have been drawn 🏆
— The SSE Women’s FA Cup (@SSEWomensFACup) 18 February 2019
These ties are due to be played on 17 March 📅 pic.twitter.com/A7vViWjgun
Ties are scheduled to take place on 17 March.
Ticket details will be released in due course.
