The champions were held by the leaders during an explosive 237th meeting between the Merseyside neighbours at Goodison on Saturday.
The Reds were unhappy with two key decisions made by VAR David Coote and his assistant Lee Betts, reports the Liverpool Echo.
And it is understood Liverpool have formally asked for an assessment of the failure to scrutinise the potential red-card challenge by Everton goalkeeper Jordan Pickford on Virgil van Dijk that left the defender visiting hospital for scans on what could be a serious knee injury.
No penalty was awarded with Van Dijk having been subsequently adjudged offside a split-second earlier by VAR.
Liverpool have also expressed the need for clarity on which part of Sadio Mane's body was deemed offside the moment VAR chose to freeze the frame before wiping out what would have been a dramatic injury-time winner from Jordan Henderson.