The Reds will travel south to face the Championship side, with the tie set to take place on Sunday 19 March.
Marc Skinner's side safely confirmed our progression to this stage thanks to a 5-0 win over Durham on Sunday, with Vilde Boe Risa, Leah Galton, Hannah Blundell, Alessia Russo and Nikita Parris all on target.
The draw was made live during BBC's The One Show on Monday evening.
Having only previously once reached the quarter-final stage - back in our inaugural 2018/19 season - United will hope to go one step further after a superb campaign so far.