Rovers Ladies will face Birmingham City Women at home in their first FA Women's Continental Tyres League Cup Group Stage fixture of 2020-21.
The Blues host Carla Ward's Barclays FAWSL team at The Sir Tom Finney Stadium, Bamber Bridge on Wednesday 7 October (kick-off 7:45pm).
Gemma Donnelly's side will then travel to Farley Way Stadium, also the venue for Rovers' first league match of this season, to play fellow Championship opposition Leicester City Women on Wednesday 4 November (kick-off 7:45pm).
Group E concludes with the final game between Birmingham and Leicester on Wednesday 18 November.
The top placed team from each of the six groups will qualify for the quarter-finals, along with the two best runners-up.