Petraeus, 60, resigned this week after admitting he "showed extremely poor judgment by engaging in an extramarital affair" with his 40-year-old biographer, Paula Broadwell, who is married to a doctor and has two children.
The Los Angeles Times reported Jill Kelley of Tampa, who it described as a State Department liaison to the military's Joint Special Operations Command in Tampa, Fla., told the FBI about the emails, which investigators then traced to Broadwell. Officials have said Kelley, who was described as a close friend of Petraeus, was considered by Broadwell to be a rival for the CIA director and retired general's affections, the newspaper said.
The New York Times reported a close friend of the Petraeus family said Kelley, 37, has been a friend of Petraeus and his wife Holly for more than five years.
The family friend described Kelley, who also is married to a doctor, as "a very well-known person of influence in the Tampa community" who is active in organizations that support military causes.
The Kelleys issued a statement Sunday night that did not address their involvement in the government investigation, The New York Times said.
"We respect his and his family's privacy, and want the same for us and our three children," the couple said.
Sources who didn't want to be identified told CNN the FBI opened its investigation into Petraeus after receiving a complaint about Broadwell's allegedly abusive emails.
Petraeus was scheduled to testify Thursday about the Sept. 11 attack on the U.S. Consulate in Benghazi, Libya, that killed four Americans. Instead, acting CIA Director Michael Morell will speak to the Senate Intelligence Committee.
That didn't sit well with House Homeland Security Committee Chairman Peter King, R-N.Y., CNN said.
"David Petraeus' testifying has nothing to do with whether or not he's still the CIA director, and I don't see how the CIA can say he's not going to testify," King said. "He was at the center of this, and he has answers that only he has."
On "Fox News Sunday," Senate Intelligence Committee Chairwoman Dianne Feinstein, D-Calif., backed off her earlier statement that President Obama should not have accepted Petraeus' resignation, the Los Angeles Times said.
"When you realize additional complications ... I think he did the right thing," she said. "I think the president really had no choice but to accept that resignation."