The semi-finals draw took place on Thursday afternoon and was made by former England international Gemma Davison.
United's reward for a fine 1-0 win over Arsenal is a meeting with another London side, with Manchester City and Tottenham meeting in the other tie.
Marc Skinner's in-form side beat WSL leaders Arsenal with an 85th-minute header by Alex Russo separating the sides in a hard-fought encounter.
The clean sheet was a fifth on the spin in all competitions, with victory secured in each of those outings.
SEMI-FINALS DRAW
Ties to be played on 2/3 February 2022.