During a meeting attended by key members of all 20 Premier League clubs, officials were presented with an update on the non-live VAR trials taking place.
They were also given "key learnings" from VAR's use in the FA Cup and League Cup this season.
VAR was used at the 2018 World Cup in Russia, where 335 incidents were checked by VAR officials, and is already underway in some other European leagues.
A formal Premier League request will now be made to the International Football Association Board and FIFA, the world governing body.
A statement from the Premier League said its testing programme would continue for the rest of the season, "with a continued emphasis on those Saturday afternoons which have several matches being played concurrently".
How VAR decisions are communicated to fans in the stadium will be addressed, with the development of a "clear protocol" to be established.
In April, Premier League clubs voted against the introduction of VAR for the 2018-19 season.
But there have been growing calls from managers and players for VAR to be introduced into the English top-flight for several years.
On Saturday, Southampton forward Charlie Austin called for VAR after he was denied a goal for offside against Watford, a decision he called a "joke".
Also last weekend, Slavisa Jokanovic, since sacked as Fulham manager, was furious after Aleksandar Mitrovic was denied a goal by a controversial offside decision, with Liverpool going straight down the other end to take the lead.
VAR is used to check goals, penalties -- both awarded and not, direct red cards and cases of mistaken identity when a player is wrongly booked or sent off.
The referee has the information relayed through his earpiece by the VAR team.
For some incidents, he can review the footage on a pitch-side television monitor before deciding whether to change his initial call.