Liverpool face the prospect of being thrown out of the Carabao Cup for fielding an ineligible player in last week's win over MK Dons.
However, the Daily Mail is reporting that Liverpool believe the FA are to blame and that the club will be given a lesser punishment.
The usual sanction would be expulsion from the competition for using a player who isn't eligible.
Pedro Chirivella has been identified as the player at the centre of an EFL investigation.
The FA's stance is usually that it is the responsibility of the clubs to make sure all their players are eligible to play.
It is thought the 22-year-old, who came on as a 63rd-minute substitute for Naby Keita, did not have the necessary international clearance to play in the match.
Liverpool say they applied for an international transfer certificate for Chirivella when he returned to Anfield from a loan spell in Spain with Extremadura last summer.
A club statement said: "The club are aware of a potential administrative issue pertaining to one of our players."
"We are working with the relevant authorities in order to establish the facts of the matter and will be making no further comment until this process is complete."