The Blues will host the Seagulls at the Academy Stadium, having topped Group One North with 14 points from five games.
Brighton finished as runners-up of Group 2 South with ten points.
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The two sides have met twice competitively - once in the FA Cup last season, with City triumphing 2-0, and again in October of this year's Women's Super League campaign, as a Georgia Stanway hat-trick fired Nick Cushing's side to a 6-0 victory.
The pair lock horns again in Manchester in the league on 27 January 2019 at 2pm.
City won the Conti Cup in 2014 and 2016, with triumphs over Arsenal and Birmingham, and reached the final in 2018.
The quarter-final tie will be played on 9/10 January with ticket information to be announced in due course.