They have proposed a points deduction rather than a fine, according to the Daily Mail.
Other clubs, though, believe a points deduction isn't practical as it would prompt a lengthy and potentially messy legal battle.
The report also claims that the Premier League board are under pressure to get the matter resolved before the clubs' end-of-season shareholders' meeting next week.
The European Super League was widely condemned by governing bodies, critics and fans.
UEFA president Aleksander Ceferin slammed the competition, ridiculing the ESL's founder clubs.
In a UEFA report, he wrote: "This report outlines how broadcast penalties, empty stadiums, reduced commercial revenues, and the collapse in transfer profits have led to a projected €8.7bn (£7.5bn) shortfall in professional club revenues, with pain shared equally among top and lower-tier clubs, only partly compensated by cost savings.
"Competition structures that destroy value, offering to give with one hand while taking away with five hands, are certainly not the answer.
"The whole football ecosystem, at professional, amateur and youth levels, has been heavily disrupted by the pandemic.
"This requires concerted efforts and a co-ordinated response throughout the football pyramid. Solidarity, not self-interest, must prevail and will win the day."
Featured Image Credit: PA
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