"Section 811 does not assert a violation of criminal law," Aftergood said.
FBI Director James Comey said last month that it was possible that "hostile actors gained access" to Clinton's emails, since she had "extensively" used her personal email while traveling abroad.
But Comey added that the agency did not find "direct evidence" that Clinton's private server "was successfully hacked."
The letters sent by the FBI to the State Department were dated Oct. 23, 2015, and Jan. 20, 2016, and marked "for official use only," Vice News reports.
They were written by Peter Strzok and Charles Kable IV, who head the FBI's counterespionage section. They were sent to Gregory Starr, the assistant secretary at the State Department's Bureau of Diplomatic Security.
They were written during the FBI's investigation into Clinton's private server use.
In the October letter, Kable wrote: "The potential compromise was identified when, as part of a Freedom of Information Act (FOIA) request, the U.S. Department of State (DoS) and the ICIG reviewed electronic mail (email) communications from the private email accounts previously used by a former Secretary of State during her tenure at DoS.
"An initial review of this material identified emails containing national security information later determined by the US Intelligence Community to be classified up to the Top Secret/Sensitive Compartmented Information Level," he wrote.
Kable had asked Starr to review a DVD the FBI had sent containing the emails and to review the classification statue of the communications, Vice News reports.
He requested that the department "de-conflict" its response with any other review requests that it had received from other government agencies, according to the report.