The investigation, first reported by the Albany Times Union, is in its initial stages. Subpoenas have been issued, the sources said.
The FBI declined to comment, as did the U.S. Attorney's Office for the Eastern District of New York.
The full scope of the investigation is not immediately clear, though the sources said there was a particular interest in nursing homes, which have been a source of increasing frustration for Cuomo.
Last week, an aide conceded the administration withheld the nursing home death toll from state lawmakers out of fear it would be used against the state by the Trump Administration.
ALSO READ | Gov. Cuomo insists nursing home COVID data was accurate, blames 'raw politics'
This week, Cuomo conceded his handling of nursing home fatality data created a "void" that became filled by misinformation and conspiracy theories but he declined to apologize.
Nursing home deaths have dogged Cuomo for months. At the onset of the pandemic, state health officials directed nursing homes to accept residents recovering from the virus as they were discharged from hospitals.
The directive was rescinded several weeks later, but Cuomo faced criticism it contributed to a high level of death in nursing homes.
The governor said he based the decision on federal guidance at the time and insisted staff members, not residents discharged from hospitals, brought coronavirus into nursing homes.
Meanwhile, some lawmakers are also calling on the National Academy of Television Arts and Sciences to vacate Cuomo's Emmy.
"Throughout this pandemic, Gov. Cuomo cared more about his moment in the spotlight than the lives of thousands of New Yorkers, and the Academy needs to stand up and recognize his role in the tragedy that took countless loved ones away from us," Assemblyman Chris Tague said. "The actions our governor took this year are nothing to celebrate, and him retaining his award in the wake of this report would be an insult to the thousands of families who lost those close to them due to the governor's actions."
Some lawmakers have called for revoking Cuomo's emergency powers.
"It is clear that what is happening here is criminal, the Governor's emergency powers need to be revoked, and there must be an investigation into the implementation of the policy, the cover up, and the continued attempts to avoid necessary transparency and accountability for grieving New York families," Rep. Lee Zeldin said in a statement following reports of the FBI investigation.
ALSO READ | Assemblyman alleges Cuomo threatened him over nursing homes scandal
MORE CORONAVIRUS COVID-19 COVERAGE
New York City COVID-19 Vaccine Tracker
New Jersey COVID-19 Vaccine Tracker
Find out if you are eligible and where you can go to get your vaccine
Do you have coronavirus symptoms?
Where to get tested in New York, New Jersey and Connecticut
WATCH: Eyewitness to a Pandemic
Centers for Disease Control and Prevention on coronavirus
Submit a News Tip or Question