Scholes said an independent survey commissioned by the Premier League, with 1,300 respondents, showed “four out of five want to keep VAR”.
He added: “That says one in five would get rid of it and that’s a big minority. And most of the four out of five say we need to improve it.”
The Football Supporters’ Association (FSA) challenged this claim, saying it made the Premier League “appear to be in denial”.
The FSA said its own research on VAR “has shown it is deeply, deeply unpopular with match-going fans”.
Premier League sources told BBC Sport it is willing to share details of the survey with the FSA, that it is not complacent about the results, and is focused on the one in five fans who want to get rid of VAR.
BBC Sport understands only one in 10 of the match-going attendees said they would keep VAR in its current form.