Academy coach Mick O'Brien, a former player with Torquay, is alleged to have struck Everton Ladies' second-choice goalkeeper Danielle Hill outside the Blue Bar in the city's Albert Dock last Sunday.
However, it is understood there are conflicting reports over who threw the first punch and both have been suspended while the matter is looked into.
Everton are not commenting on the allegations.
Police have confirmed they have received a complaint which they are currently investigating.
"Merseyside Police can confirm an investigation is under way following the assault of a 24-year-old woman in Liverpool city centre on Sunday, December 16," said a statement.
"The incident occurred near to the entrance of the Blue Bar.
"An investigation into the full circumstances of the incident is ongoing."
- Crime & Justice
- Sports & Recreation
- Everton Ladies
- Danielle Hill