The clubs are threatening legal action against the league over their finances.
Both clubs wrote to the league last week about the recent accounts ofEverton, which showed losses for the 2020-21 season.
Over the past three years, they have posted losses.
League profitability and sustainable rules allow for losses over a three-year period.
Over the past two seasons, Covid-19 losses amount to 170 million dollars.
It dwarfs clubs of a similar size, which has caused surprise among some teams.
Over the past two seasons, the Covid-19 losses have been posted by both Newcastle and Villa.
The Toffees secured their status in the top flight on Thursday with a win over Crystal Palace.
They are confident that they are in compliance with the rules of the league.
An independent commission is needed to assess the finances ofEverton.
It is believed that the matter is being viewed as one of sporting integrity because of the amount of money the club spent in the last transfer window.
When contacted by the British Broadcasting Corporation, the League declined to comment.
When releasing their accounts in March, they said their actual losses were about 170 million dollars over three years, with the figure calculated as an average over the last two seasons.
Spending on their new stadium and on the women's team bring their finances into line, as well as other costs.
In March, the club said they remained in a secure financial position, after further support from their owner, Farhad Moshiri.
The UK government and the European Union have imposed sanctions on Alisher Usmanov, a Russian billionaire.
The naming rights of the unbuilt stadium which is set to open in 2024 was paid for by Usmanov, who is a close business associate of Moshiri.
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