The draw for the last eight takes place at Wembley Stadium, from 18:30 GMT.
United booked our spot with a convincing 6-0 victory at Wolverhampton Wanderers, as Mared Griffiths came off the bench to score twice on debut, after goals from Elisabeth Terland, Leah Galton, Aoife Mannion and Ella Toone.
The rest of the top four in the Women's Super League will also be present, as leaders Chelsea dispatched Everton 4-1.
Arsenal and Manchester City also won on Sunday, getting past London City Lionesses and Leicester City respectively.
Top-flight sides Aston Villa, Crystal Palace and Liverpool are in the hat too, while there is lower-league representation in the form of Sunderland, who beat Portsmouth in an all-Championship clash.