Washington (CNN) The federal prosecutor leading the probe into the 2016 Trump-Russia investigation has begun examining the role former CIA Director John Brennan played in how the intelligence community assessed Russia's election interference, according to The New York Times .

Representatives for Brennan, the Justice Department and a spokesperson for the CIA all declined to comment to the Times. The CIA also declined additional comment to CNN on the matter. CNN has reached out to the Justice Department and Brennan's lawyer for comment.

Durham is interested in what Brennan told other officials -- including former FBI Director James Comey -- about his and the CIA's views of the infamous dossier compiled by retired British spy Christopher Steele of salacious allegations about Donald Trump, Trump associates and Russia, according to the newspaper.

The Times reported that Durham is also looking into whether Brennan privately contradicted his public comments, including a May 2017 hearing before Congress, about "both the dossier and about any debate among the intelligence agencies over their conclusions on Russia's interference."

Sources stressed to the Times that Durham's inquiry into Brennan is continuing and it is so far unclear what he has uncovered.

During a panel at the George Mason University in October, Brennan said that he has "no qualms whatsoever" and would be "happy" to talk to investigators he hopes are conducting the review "in a fair and appropriate manner," adding that Durham has a "good reputation."

Brennan also said he's "very confident" the CIA "conducted its responsibilities appropriately, consistent with our legal authorities, and in the matter that was apolitical."

The US intelligence community concluded in a January 2017 assessment that Russian President Vladimir Putin ordered an "influence campaign" aimed at hurting Democratic nominee Hillary Clinton and helping Trump in the 2016 presidential election.

"All three agencies agree with this judgment. CIA and FBI have high confidence in this judgment; (National Security Agency) has moderate confidence," the 2017 report said.

Brennan said during a 2017 House Intelligence Committee hearing that his agency did not rely on the Steele dossier to reach its conclusions in the intelligence assessment.

Durham and his investigators are also trying to learn more about any debate within the CIA over the January 2017 intelligence report and any discussions that led intelligence chiefs to include the Steele dossier in the report's appendix, the Times reported.

report by the Justice Department inspector general released last week found that the CIA, including Brennan, expressed concern over, including Steele's allegations.

Comey and his No. 2, former deputy FBI Director Andrew McCabe, had argued that Steele's information should be included in the intelligence community assessment -- despite acknowledging that many of the claims had still not been independently verified by the FBI, the report found.

The report had also concluded that the FBI was justified to open the Russia investigation in July 2016, and that top FBI officials weren't motivated by political bias against Trump.

In a statement that was unusual for a prosecutor conducting an ongoing investigation, Durham undercut the inspector general's findings about a lack of political bias, saying "we do not agree with some of the report's conclusions as to predication and how the FBI case was opened."

Trump has criticized Brennan, who held the role of CIA director under President Barack Obama, while Brennan, since leaving office, has been outspoken against the President.

The President has publicly called for investigations into Brennan, among other former intelligence chiefs.

Conservatives have argued that the Trump-Russia investigation has been tainted by the use of the Steele dossier, including to apply for a FISA warrant into a former Trump campaign associate. Since the dossier has been released, some of the claims have been debunked, others have held up over time; some remain unproven, and other parts are partially true.

The criminal investigation into the intelligence and origins has been driven by Barr's suspicions that some of the officials overseeing the counterintelligence probe of the 2016 Trump campaign may have acted improperly.

Barr's concerns have aligned with Trump's unsubstantiated claims that he is the victim of a "deep state" operation that has tried to disrupt his presidency.