The Toffees are one point and one place behind Leeds in the battle for survival but the Merseyside club have played two fewer games.
Frank Lampard's side have lost four of their last five league games - their only victory came against Leeds - and problems off the pitch could potentially come into play with a number of teams involved in the relegation scrap.
According to the Daily Mail, the club could face a points deduction over a breach of the Premier League's profit and sustainability rules, which state that clubs are only allowed to lose a maximum of £105m over three years.
Everton recorded combined losses of over £260m between 2017 and 2020, which would normally be seen as a clear breach of the guidelines.
However, the impact of the Covid-19 pandemic means the spending rules have been changed with the three-year assessment period extended to four. The two seasons in which clubs were most impacted by Covid-19 will be taken as one season, with an average figure over both campaigns being used in the assessment.
The Toffees are yet to publish their accounts for the 2020-21 season as they reportedly seek clarification from the Premier League over what percentage of their losses can be offset by the impact of Covid-19 on football.
The club are anticipated to report further losses in their latest accounts, with the Premier League giving all clubs a deadline of later this month to publish their latest accounts.
The Liverpool Echo have reported that Everton are not concerned about a potential points deduction and are confident they have been compliant with the competition's rules.