Having reached the final of the competition last season, Marc Skinner's side will be looking to go one better this time.
Women's Super League clubs enter at the fourth-round stage and, in the draw on Tuesday, the Reds were pitted against Newcastle United.
Ties will take place on Sunday 14 January 2024, with the match set to take place at Leigh Sports Village.
It will be the first time the sides have ever met, with United having formed in 2018 and Newcastle Women only recently becoming officially part of Newcastle United.
The draw also threw up some other big ties, with Championship side Durham hosting Manchester City and an all-WSL clash in the form of Chelsea v West Ham.