The New York Times on Friday quoted an unnamed official as saying prosecutors had recommended felony charges against the former general, who quit his CIA post in 2012 after admitting he had an affair with Paula Broadwell, an army reserve officer, while she was writing his biography.
The Associated Press later similarly reported that charges were being considered, quoting its own confidential source.
Federal investigators have been looking into whether Petraeus provided classified information to his biographer. A lawyer for Petraeus declined to comment on Friday night, as did the justice department and the FBI.
The justice department investigation has focused on whether Petraeus gave Broadwell access to his CIA email account and other highly classified information.