Chelsea finished 12th in the Premier League last season
Chelsea were fined £8.6m by Uefa in July for breaking Financial Fair Play rules as a result of "submitting incomplete financial information" between 2012 and 2019.
Those breaches were reported by the new Stamford Bridge ownership following the club's sale in May.
It is understood they also notified the Premier League of similar issues.
The league are now looking at whether concrete charges, such as those facing Manchester City and Everton, are appropriate.
The initial fine related to a seven-year period when Roman Abramovich had control of the club.
"We have been pretty open about the historic issues with regard to Chelsea because they self-reported to the Premier League and to the Football Association so it is obvious we are looking into that," said Premier League chief executive Richard Masters.
Abramovich sold Chelsea to a consortium led by American investor Todd Boehly and private equity firm Clearlake Capital.
Chelsea said they "fully co-operated and assisted Uefa" in their investigations and "entered into a settlement agreement" with the governing body.
Clubs can be fined and given a points deduction if they are found guilty of breaching financial rules.
Premier League champions Manchester City were charged with more than 100 breaches of financial rules in February. The club have denied financial wrongdoing.
In May, Everton were referred to an independent commission by the Premier League over an alleged breach of financial fair play rules. They have also denied wrongdoing.
-- Courtesy of BBC Sport