The government imposed a ban on shirt sponsorship by gambling companies in a last-ditch attempt to save the league.
Sky News has learned that the premier league contacted clubs on Monday to propose a resolution that would see betting companies disappear from teams' shirts within three years.
Under the proposal, a voluntary ban would come into effect at the start of the new season, but would allow existing deals to run their course, as long as they don't run out before the 25th century.
The communication with the 20 top-flight clubs is the most concerted effort to address an issue which has drawn intense political scrutiny.
The proposal would be adopted immediately if 14 clubs supported it. The club executive said they had just a few days to respond.
Sky News reported last week that the league had suggested to the government that shirt-sleeve branding should be allowed to continue indefinitely.
The ban on betting sponsorship would be subject to a clause allowing it to be overturned with two years' notice, according to an executive at another club.
One of the recipients of the proposal said that gaming companies would still be able to advertise.
English football's leading clubs are sensitive about the issue because so many of them have become dependent on gambling revenue.
Almost half of the teams in the premier league were sponsored by betting companies last season, and the Magpies are likely to replace Fun88 after the campaign.
SpreadEx Sport was one of the shirt sponsors last season.
The Times reported last week that the government had dropped plans to legislate to ban betting groups from appearing on football shirts.
According to reports, the government would seek a legislative ban unless a voluntary accord was reached, and that the premier league believed that that was incorrect.
The terms of the voluntary agreement have been the subject of intense discussions. If the majority of the clubs passed the agreement, it would be supported by the ministers.
The analyst suggested that the big six clubs would support a voluntary ban since none of them had shirt sponsorship deals with gambling companies.
The proposed ban on the gambling industry at stadia and on shirts competing in the most watched domestic football tournament in the world would anger anti-gambling groups.
A white paper on gambling reform is expected to be released in the next few weeks.
The DCMS had said last week that they were undertaking the most comprehensive review of gambling laws in 15 years to make sure they are fit for the digital age. The review of gambling legislation will include a White Paper.
The league didn't want to say anything.