The request follows on from days of debate surrounding the officiating in the Reds' 2-1 defeat by Spurs.
The refereeing body admitted "a significant human error" in VAR's decision not to allow Diaz's goal which would have given Liverpool the lead against Tottenham.
PGMOL head Howard Webb has also reached out to club privately to apologise, while Liverpool themselves released a statement saying "sporting integrity was being undermined" and that the club would be "exploring their options".
VAR officials Darren England and assistant Dan Cook mistakenly believed Diaz's goal was initially allowed to stand and told on-field referee Simon Hooper their check was complete.
They failed to rectify their mistake in time and referee Hooper was unaware of any issue until half-time.
"Liverpool Football Club acknowledges PGMOL's admission of their failures last night. It is clear that the correct application of the laws of the game did not occur, resulting in sporting integrity being undermined," read the statement.
"We fully accept the pressures that match officials work under but these pressures are supposed to be alleviated, not exacerbated, by the existence and implementation of VAR.
"It is therefore unsatisfactory that sufficient time was not afforded to allow the correct decision to be made and that there was no subsequent intervention."
England and Cook were subsequently stood down from their remaining scheduled fixtures on Sunday.
They were also reported to have been allowed to travel to and from the UAE to work on a midweek fixture there.
PGMOL said the Diaz incident "was a clear and obvious factual error and should have resulted in the goal being awarded through VAR intervention".
