Petraeus aides and other high-ranking military officials were often told by Petraeus when he was chief of U.S. Central Command to provide military records and other documents to Paula Broadwell for her work on Petraeus' 352-page biography "All In," former staff members and other officials told the Post.
Petraeus and Broadwell, who are both married and had an affair at the time, have told the FBI Petraeus did not provide her with classified information, law enforcement officials have said.
But investigators are looking into a possible distinction between providing the classified information and tasking others to do so.
Some former Petraeus staff members told the newspaper they were irritated and alarmed by Broadwell's persistent requests for information, which sometimes involved sensitive material.
One former Defense Department official said that when staff at the Kabul headquarters of the NATO-led coalition forces in Afghanistan questioned Broadwell's access to certain classified material, she assured them Petraeus had OKd her seeing it.
"Even if he did not directly give her classified information, he was allowing his name to be used," the unidentified former official told the Post. "I would be surprised if anyone would raise a question for anything below 'top secret.'"
Broadwell maintained a "top secret" security clearance as an officer in the Army reserves.
FBI agents discovered low-level classified material on her computer in late summer and found additional classified documents after searching her Charlotte, N.C., home Nov. 12, officials have said.
The documents are described as sensitive but relatively harmless, the Post said, citing officials who said they were mostly schedules and PowerPoint presentations classified as "secret."
But even low-level classified records are generally not permitted to be kept on someone's personal computer or in their home.
Two days after the FBI search of Broadwell's home, the Army suspended her security clearance.
Petraeus and Broadwell lawyers declined to comment on the Post story, as did Broadwell spokeswoman Dee Dee Myers and the FBI.
Petraeus, a retired four-star general, resigned as CIA director Nov. 9 because of the affair.