Barr is working in close collaboration with CIA Director Gina Haspel, Director of National Intelligence Dan Coats and FBI Director Christopher Wray, the source said.
Trump often called for the Justice Department and others to review how the FBI began investigating the connection between his campaign and Russian meddling in the 2016 election. He told reporters Tuesday he did not direct Barr to call on intelligence agencies to join his review of the Russia probe.
"But I think it's a great thing that he did it. I saw it last night, and they want to look at how that whole hoax got started," he continued. "You know what? I am so proud of our attorney general, that he is looking into it. I think it's great."
As CNN previously reported
, US attorney John Durham in Connecticut is heading up the effort with Barr. The source said Durham and Barr are doing a comprehensive review, and Durham is with working with the Justice Department's Inspector General, Michael Horowitz, as well.
"I think spying on a political campaign is a big deal," Barr told Congress then.
He later defended the term
, saying at a separate hearing that he used it because "it is the broadest word incorporating really all forms of covert intelligence collection."
"Many people seem to assume that the only intelligence collection that occurred was a single confidential informant and a FISA warrant," Barr said, testifying before the Senate Judiciary Committee earlier this month. "I'd like to find out whether that is, in fact, true. It strikes me as a fairly anemic effort if that was the counterintelligence effort designed to stop the threat as it's being represented."
US Attorney John Huber in Utah is no longer involved on Russia issues. Huber had originally been tasked
with looking at allegations of surveillance abuse by former Attorney General Jeff Sessions, but has been in a holding pattern as the inspector general completes his review of the surveillance warrant the FBI obtained on Trump campaign foreign policy adviser Carter Page.
Huber's review of other issues related to Hillary Clinton and the Clinton Foundation is nearing completion, the source said.
The DNI and CIA did not immediately respond to a request for comment.
Trump and his GOP allies on Capitol Hill repeatedly claimed -- without evidence -- that a warrant obtained in 2016 to allow the FBI to monitor Page was evidence of surveillance abuse by the Justice Department and FBI.
Conservative critics of special counsel Robert Mueller have argued that his work sprang from the fruit of a poisonous tree, suggesting that the FISA warrant application was tainted because it included some of the dossier compiled by retired British spy Christopher Steele that was paid for by Democrats. They also point to the FBI's use of an informant to meet with former Trump campaign adviser George Papadopoulos.
Democrats, however, say the FISA warrant on Page was justified because of his contacts with Russia and that the FBI and Justice Department followed proper protocols in successfully getting the Foreign Intelligence Surveillance Court to approve the warrant and subsequent renewals.
This story has been updated.
CNN's Veronica Stracqualursi contributed to this report.