That Allen remains in command in Afghanistan suggests that there is no criminal issue, a U.S. official told CNN. But the official said the Defense Department's inspector general could still find evidence of criminal conduct.
Kelley has not responded publicly to the latest news.
Both Allen and Petraeus appear to know Kelley's sister, Natalie Khawam. The men wrote letters in support of the sister in a custody battle, court records show.
On Monday, FBI agents were at Broadwell's home in Charlotte, North Carolina, according to spokeswoman Shelley Lynch. She declined to say what the agents were doing there.
A senior law enforcement official close to the Broadwell investigation said Wednesday night that it appeared unlikely she would be prosecuted for any unauthorized release of classified information.
The official told CNN National Security Contributor Fran Townsend that investigators were reviewing materials taken Monday from Broadwell's home, but that the information in question did not appear to be substantial; there may have been a technical violation but, if so, it was not egregious.
Broadwell had previously turned over a computer to investigators.
The official said Broadwell agreed to the search of her home but that officials also had secured a search warrant.
The official stressed the decision whether to prosecute rests with the Justice Department.
A source told CNN that Broadwell was acting as Petraeus' archivist and that the FBI had gone to her house to look for any documents she might have.
As a commissioned officer in the military reserves, Broadwell would have had "secret" or "top secret" security clearance, military officials said.
Access to information would have depended on what she needed to know to carry out an assigned task, said the officials, who would not go on the record about an ongoing investigation.
Broadwell has said that she was working on a second book about Petraeus. Her LinkedIn profile lists her as "Archivist/Biographer for General (Retired) David Petreaus." Her first book, "All In," was about Petraeus' leadership.
Broadwell has spoken about how she had to deal with sensitive information in the course of researching the first book.
"I had to follow very clear lines of non-disclosure and sign non-disclosure agreements, like my colleagues. I felt like I was almost held to a higher level of accountability because I could lose my clearance," Broadwell said in a speech last year. "I think it was important to inform my writing, but I knew there was a clear line that I couldn't cross when I was writing it out."
Petraeus has said he never shared classified information with Broadwell, said retired military officer John Nagl, who cited conversations in recent days with Petraeus.
Broadwell, a military intelligence reservist, is assigned to West Point, the Army's military academy, according to her service record, which lists her assignment as "United States Military Academy Staff & Faculty." In August, she was promoted to lieutenant colonel.
Last month, during a speech at the University of Denver, Broadwell suggested the Sept. 11 attackers in Libya were targeting a secret prison at the Benghazi consulate annex, raising unverified concerns about possible security leaks.
"I don't know if a lot of you have heard this, but the CIA annex had actually taken a couple of Libyan militia members prisoner and they think that the attack on the consulate was an effort to get these prisoners back," she said.
A senior intelligence official said no prisoners had been held at the annex. Broadwell did not provide a source for her information, and no evidence has emerged that it came from Petraeus.
Administration officials have said the Benghazi assault was a terrorist attack.