Half of last season’s 20 top-flight teams had betting sponsors on their shirts, with the government hoping to decide on a ban before 21 July.
The Premier League is supportive of a voluntary move where gambling sponsors are phased out within three years.
But 14 of its 20 clubs would need to vote in favor for it to be approved.
An email was sent to clubs on Monday, with a decision expected within the next week.
Last week, government sources said a final decision was yet to be made and that a ban on shirt sponsorship was still on the table.
But it is understood that a voluntary ban has been discussed and could offer a middle ground for clubs and avert any legislation on a much-debated topic.
Everton and promoted side Bournemouth have both recently signed new shirt deals with betting firms, while Crystal Palace have dropped theirs in favor of a car retailer.
A voluntary move is likely to disappoint campaigners, who have been urging the government to act and impose a ban which would also include league and social media sponsorship, plus pitch-perimeter advertising.
A University of Glasgow study claimed that more than 700 betting-related logos can be seen during the course of a match.
The Premier League declined to comment.
Its clubs are likely to be less affected by a ban because they can draw on other types of sponsorships. But the English Football League, sponsored by Sky Bet, has said it would cost their clubs £40m a year.
It is not believed that a ban would affect EFL clubs, but choosing only top-flights clubs has been described as “incoherent” by campaigners and has been a point of contention for the Premier League.
A spokesperson for the Department of Culture, Media and Sport said: “We are undertaking the most comprehensive review of gambling laws in 15 years to make sure they are fit for the digital age.
“We will publish a white paper which sets out our vision for the sector in the coming weeks.”