Liverpool have contacted the FA claiming Manchester United fans sang offensive chants during their Women's Super League game in Leigh on Saturday.
In their match report to the FA, Liverpool Women highlighted abuse they say was aimed at manager Vicky Jepson, as well as the club in general.
Manchester United say they are aware of the allegations and will be investigating.
The two clubs were meeting for the first time in WSL history after United were promoted from the Championship in May.
Casey Stoney's side took all three points as second-half goals from Lauren James and Katie Zelem earned United a 2-0 home win at Leigh Sports Village.