This week's Carabao Cup quarter-finals went ahead without the use of VAR despite each game being played at a Premier League ground, where the technology is available.
Until now, the EFL has only used the review system in the League Cup semi-finals and finals, in addition to its play-off finals, but this could be about to change.
According to The Times, the governing body is considering a low-cost VAR alternative for English football's second to fourth tiers.
A system called Football Video Support (FVS) is currently being trialled, which would allow managers to call for a challenge when they dispute a decision.
Similar to the technology used in cricket and tennis, each team would be allowed two unsuccessful challenges per match.
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Having already been tested in the FIFA Women's Under-17 World Cup in October, the International FA Board (Ifab) is now set to extend its trial, in the hope it could be suited to the EFL's competitions.
An EFL spokesperson said: "The league continues to monitor developments in the work of IFAB and emerging technologies to support match officials.
"While we are mindful of the impact on the authenticity of the match-going experience for supporters, and the implementation costs for clubs, it is something we continue to keep under review.
"Any changes would require detailed discussion and approval from our clubs."
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At present, goal-line technology is in use in the Championship, but not League One or League Two, where appetite for VAR is said to be particularly low.
However, a number of Football League clubs will soon have an introduction to the officiating system.
The FA recently revealed that VAR will be used in every FA Cup game from the fifth round onwards, a first for the competition.
Most top leagues in Europe have adopted VAR, but Sweden voted against its introduction earlier this year.
Meanwhile Norway's league and football association are set to vote in March over whether it should be scrapped, following fan protests at a top-flight game between Rosenborg and Lillestrom.
FVS is believed to be a less controversial use of technology, with legendary former referee Pierluigi Collina, who is now chairman of FIFA's referees committee, previously backing its trial.
Speaking to ESPN last month, he said: "We are at the beginning of the trial and the experiences at both the U20 and U17 FIFA Women's World Cup will be carefully analysed but so far, we haven't noticed anything unexpected."
Collina was also keen to highlight the difference between FVS and VAR, adding: "Making clear that FVS is not VAR is critical, in particular in terms of expectation.
"Because of the limited number of cameras, FVS won't be able to show what VAR can show.
"Offside is an example: without cameras properly positioned, only clear offside can be spotted. This makes the on-field decision important too.
"FVS is designed to work with a limited camera set up, ideally up to four to five. With more cameras, the process of checking all of the footage and available angles may become very long as, and differently from VAR, there are not any video match officials selecting those clips to be seen by the referee."