Liverpool have asked PGMOL for audio of discussions between the match officials in Saturday's 2-1 defeat by Tottenham.
The video assistant referee failed to overturn an incorrect decision to disallow a Luis Diaz goal for offside.
PGMOL, the governing body for referees, said the decision to rule out the goal was "a significant human error".
On Sunday, the Reds released a statement saying the explanation was "unacceptable" and that "sporting integrity has been undermined".
The club called for a "review with full transparency" and added they will "explore the range of options available given the clear need for escalation and resolution".
Darren England, who was on VAR duty during the game at the Tottenham Hotspur Stadium, and assistant VAR Dan Cook were stood down from duty for the rest of the weekend because of the error.
PGMOL recognised the two VAR officials failed to act correctly after Diaz's 34th-minute strike was wrongly ruled out for offside. The game was at 0-0 at that point, with Liverpool down to 10 men after Curtis Jones had been sent off following England's intervention.
In a statement released following the controversial game, PGMOL said the Diaz incident "was a clear and obvious factual error and should have resulted in the goal being awarded through VAR intervention".
It is understood referees' chief Howard Webb has spoken to Liverpool about the incident.
Last season, Webb appeared on Sky Sports' Monday Night Football to explain the process of VAR using both correct and incorrect decisions, which allowed fans to hear the match officials' conversations for the first time in a bid to increase transparency.
This season, six audio recordings have been released from Premier League games, including Wolves' penalty appeal after Manchester United goalkeeper Andre Onana collided with striker Sasa Kalajdzic, and Liverpool captain Virgil van Dijk's red card for a foul on Newcastle forward Alexander Isak.
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