The Reds were paired with their fellow Barclays Women's Super League side during the draw for the last four on Monday afternoon.
Gareth Taylor's team secured their advancement by winning 1-0 in extra-time at Charlton Athletic the day before, while Brighton beat Arsenal 2-0 away from home.
Semi-finals are scheduled to be played on Sunday May 10.
Confirmed fixture and ticket details will be announced on Liverpoolfc.com soon.
