Officials have said revelations about the affair that led to Friday's resignation of CIA Director David Petraeus were discovered during an FBI investigation.
The Associated Press cites anonymous government officials who were briefed on the reasons behind General Petraeus' sudden resignation.
It was unclear what the FBI was investigating or when it discovered the Petraeus affair.
According to his letter of resignation, Gen Petraeus asked President Barack Obama on Thursday to allow him to resign, and on Friday the president accepted.
Gen Petraeus said he had shown "extremely poor judgement" in having an affair.
"Such behaviour is unacceptable, both as a husband and as the leader of an organisation such as ours," Gen Petraeus wrote.
He had only been sworn in as director of the Central Intelligence Agency on September 6 last year.
Prior to that, he was a four-star general with 37 years' service in the US Army.
His last assignments in the army were as commander of Isaf, the International Security Assistance Force, and commander of US forces in Afghanistan and in Iraq.
The resignation took Washington's intelligence and political communities by surprise, coming as a sudden end to the public career of the best-known general in recent years.
In a statement released after the resignation was announced, President Obama hailed the "extraordinary service" of Gen Petraeus.
"David Petraeus has provided extraordinary service to the United States for decades," Mr Obama said. "By any measure, he was one of the outstanding general officers of his generation."
The president said the CIA's Deputy Director Michael Morell would serve as acting director.
"I am completely confident that the CIA will continue to thrive and carry out its essential mission," Mr Obama said.
Gen Petraeus has been married for 37 years to Holly Petraeus, whom he met when he was a cadet at the US Military Academy at West Point.
Although the president made no direct mention of Petraeus' reason for resigning, he offered his thoughts and prayers to the general and his wife.
He said Mrs Petraeus has "done so much to help military families through her own work. I wish them the very best at this difficult time."
The CIA has come under fire in recent weeks in the wake of the September 11 attack on the US Consulate in Benghazi, Libya that killed US Ambassador Chris Stevens and three other Americans.
Critics have questioned how much the intelligence agency knew about the likelihood and nature of the attack.