Two people familiar with the matter told the news agency that members of the world football body’s executive committee were briefed on the investigation at a meeting last month.
The closed door briefing session took place in Zurich, where FIFA has its headquarters.
It comes after seven FIFA officials, including the then-FIFA vice-president Jeffrey Webb, were arrested in Zurich in May as part of a US investigation into international money laundering and other charges.
At the same time, Swiss police launched a separate criminal investigation into the award of the 2018 and 2022 World Cup tournaments.
They led FIFA President Sepp Blatter to announce his departure in an attempt to ease the crisis.
Analysts say the internal investigation may signal greater cooperation with two criminal inquiries.
The investigation is being run in parallel to the probes being carried out by authorities in the United States and Switzerland.
The American law firm that is conducting the investigation is understood to be Quinn Emanuel Urquhart & Sullivan.
French head of UEFA Michel Platini revealed two weeks ago that he plans to run for the FIFA presidency, saying he wants to restore dignity to the world governing body.
Other possible candidates include former Brazil star Zico and Argentina legend Diego Maradona, although both lack any experience of international football administration.
Candidates have until October 26 – exactly four months before the vote – to come forward.