The gambling white paper is expected to be published in the coming weeks.
In that review of gambling legislation, the government is not expected to propose banning gambling sponsorship of clubs by law.
Instead, the BBC has been told the plan is for the Premier League to agree voluntarily to changes to the front of shirts.
It is believed top-flight clubs are yet to vote on this.
The plans, which were largely agreed by former Prime Minister Boris Johnson before he stepped down, leave the way open for gambling companies to continue their involvement with football.
Betting companies are still expected to be promoted in Premier League stadiums, and also on other parts of club shirts.
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- Eight of the 20 Premier League clubs display gambling firm names on the front of their shirts, though they are banned from junior replica kits.