The tie, which is to be played at Leigh Sports Village, will kick-off at 19:00 GMT.
Each of the other three quarter-finals will also begin on the same evening, the Women's Professional League has confirmed.
United beat Liverpool, Everton and Newcastle United to top Group A in the opening stage, and will face Brighton & Hove Albion or Arsenal in the last four, should we dispose of the Blues.
The final, meanwhile, will be held at Derby County’s Pride Park on Saturday 15 March 2025 (12:15 GMT) and is set to be broadcast live on the BBC.