Could the game be replayed?
It is not clear what options Liverpool are referring to in their statement. There is no precedent in the UK for either a match result to be changed or for a game to be replayed due to a refereeing error.
A 1999 FA Cup tie between Arsenal and Sheffield United was replayed only because Arsenal boss Arsene Wenger offered that olive branch after the winning goal was scored in controversial circumstances.
What about the UAE trip?
VAR officials for the Liverpool match - England, Cook and fourth official Michael Oliver - were also part of an officiating team who took charge of a league game in the United Arab Emirates on Thursday, just 48 hours before Saturday's fixture.
The Football Association had approved the trip, with the trio arriving in London on Friday to prepare for Saturday's game.
It is understood that Liverpool also want this looked at as part of PGMOL's review.
These appointments are done on an FA-to-FA request basis and there are currently no further visits to the UAE or Saudi Arabia scheduled, though this may change.
Is this an issue?
Craig Pawson refereed Panathinaikos v PAOK in the Greek Super League on 3 May, while Andy Madley did two matches in Japan's J League and Japan's Kirin Cup match against El Salvador in June.
Both of these visits came after requests from the respective FAs. Oliver also took charge of a Saudi Pro League game in April.
The flight time to the United Arab Emirates from the UK is approximately seven hours, with a time difference of three hours.
BBC Sport's Dan Roan says: "While the FA and PGMOL both approved the request, and match officials [as well as teams] regularly go overseas for midweek European fixtures, it will raise questions as to whether fatigue from the trip to the Middle East may have played a role in their decision-making.
"The PGMOL believes such foreign assignments enhance the international standing of their officiating, and make the point that referees from other countries do the same."
Some people believe that allowing officials to work for leagues in countries with connections to Premier League clubs could lead to claims of a conflict of interest.
Nine English top-flight teams have American owners, with a 10th - Everton - having agreed a takeover deal with an American investment firm, while at least three have Middle East owners and another is in Chinese ownership.
What do the referees say?
Ref Support UK, a charity that provides training and support for referees, said: "This past weekend has probably been one of the toughest for top-flight match officials in England.
"Hopefully this will be a turning point for the game and for VAR. There will always be humans involved in the decision-making process in football, and humans, both players and referees, are fallible and will make mistakes. It's how we learn from these mistakes that will take the game forward.
"Introducing a law change to allow a match official to change a clear error after play has restarted would be a good pace to start."
President of the Referees' Association, Paul Field, said: "Players, coaches, managers and match officials don't deliberately make errors and we will wait for the PGMOL to make a detailed investigation and take whatever operational action they deem appropriate.
"We continue to be concerned about the level of abuse being aimed at match officials and remind people that comments made in the media and by pundits have outcomes at all levels of the game, but notable at grassroots."