The interviews, confirmed to the network by US officials briefed on the probe, mark a step forward in the Federal Bureau of Investigation's probe, which the officials described as nearing its end.
The investigation has focused on the security of the Clinton server and whether classified information was exchanged.
The officials said no date had yet been set for an FBI interview of Clinton, the likely Democratic presidential nominee, but that one was expected in the coming weeks, CNN reported.
Bryan PaBenghazigliano, the former State Department staffer who reportedly helped set up Clinton's server and has been granted immunity in the criminal investigation, was also expected to be interviewed.
Spokespersons for the FBI and Justice Department, as well as lawyers for Abedin and Clinton, declined to comment.
On Wednesday, federal judge Emmet Sullivan said Clinton may be required to testify about her private email system as part of a freedom of information act lawsuit brought by conservative watchdog group Judicial Watch.
Clinton's use of a private server for both official and private correspondence first came to light in 2015 during Republican-led congressional investigations into her handling of a militant attack on the US mission in Benghazi, Libya.
The assault in 2012 left the US ambassador and three other Americans dead.
The FBI has since launched a criminal investigation amid Republican charges that use of the unsecured system endangered national security.
Clinton has maintained that none of her emails had been marked "classified" when she sent them and, after her own lawyers had removed mails they deemed purely personal, she submitted a 52,000-page document dump to the State Department.
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