Samuel Eto'o and Willian Chelsea transfers under investigation
The breaches were said to have been reported by Chelsea's new owners after they purchased the club from the Russian oligarch in May 2022.
It is understood they also notified the Premier League at the same time.
Chelsea were fined £8.6 million by Uefa in July for breaking Financial Fair Play rules as a result of "submitting incomplete financial information" from 2012 to 2019.
Both players joined the club from Russian side Anzhi Makhachkala in 2013, with Willian's fee reportedly £30 million.
Eto'o joined the club for an undisclosed fee.
Abramovich owned the club from 2003 to 2022 and sold it to a consortium led by American investor Todd Boehly and private equity firm Clearlake Capital last year amid his assets being frozen during the outbreak of the Russian invasion in Ukraine.
A Chelsea statement on Monday said: "These allegations pre-date the club's current ownership. They concern entities that were allegedly controlled by the club's former owner and do not relate to any individual who is presently at the club.
"Chelsea FC's ownership group completed its purchase of the club on May 30, 2022.
"During a thorough due diligence process prior to completion of the purchase, the ownership group became aware of potentially incomplete financial reporting concerning historical transactions during the club's previous ownership.
"Immediately following the completion of the purchase, the club proactively self-reported these matters to all applicable football regulators.
"In accordance with the club's ownership group's core principles of full compliance and transparency the club has proactively assisted the applicable regulators with their investigations and will continue to do so."
