Jurgen Klopp fielded a much-changed starting XI in midweek as the Reds beat the League Two side 2-0 in their third round tie.
However, one of those included, 22-year-old Pedro Chirivella, may not have met the registration criteria - related to an International Transfer Certificate issue.
The EFL has the authority to fine or eject the club from the competition altogether, but sources told Goal that they believe there will be a strong mitigation.
"The club are aware of a potential administrative issue pertaining to one of our players," a statement issued by Liverpool said.
"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."
The Reds made 11 changes to the team that beat Chelsea 2-1 in the Premier League, as Herbie Kane and Sepp van den Berg made their debuts against MK Dons and Caoimhin Kelleher, Rhian Brewster and Harvey Elliott also featured.
Even if the Anfield outfit are found guilty of the offence, precedent suggests they are likely to be handed a fine.
The EFL hit Sunderland with a financial sanction in 2014 after they fielded striker Ji Dong-Won in the competition - also against MK Dons.
The South Korean also featured in four Premier League matches, leading to the club being fined by both bodies.
That case also related to a registration error, as the Black Cats did not realise they required international clearance to field Ji upon his return from loan at German side Augsburg.
But one of the mitigating factors in the Ji case was that Sunderland were losing when the attacker was taken off, though they then went on to win 4-2.
Sunderland went on to reach the cup final that season, where they lost to Manchester City.
Liverpool have been paired with Arsenal in the fourth round of this year’s competition and will host Unai Emery’s side at Anfield on October 30.