Barr served as attorney general from 1991 to 1993. The question is whether Barr would pass Trump's loyalty test - which proved to be Sessions' undoing, after the latter recused himself from overseeing the Russian Federation investigation.
Sources cautioned to CNN, however, that Trump makes the final decision.
After leaving the Justice Department, Barr served in a variety of high-level corporate positions, including as general counsel and executive vice president of Verizon Communications.
Barr was the general counsel of GTE when I represented that company (as one of dozens of lawyers from at least four law firms to do so) in contentious litigation following the enactment of the Telecommunications Act of 1996.
The White House declined to comment.
The Mueller probe has been an Achilles heel for the office of attorney general the past couple of years.
The former attorney general hasn't shied away from weighing in on Mueller's investigation.
Chris Evans could return as Captain America after 'Avengers 4'
Evans continued, "Part of you nearly kind of thinks: Well, if we end on the right note... and I think it really kind of does". Maybe, but Evans and the rest of the cast still have a few months to flip-flop on the issue before we all know for sure.
"What I have said, without mentioning Mr. Barr - I've said, the best thing the administration can do is to get somebody who had majority support from Republicans and Democrats alike for attorney general". He was promoted to deputy attorney general next, and then to the top role. Patrick Leahy of Vermont, a member of the Senate Judiciary Committee, which would hold hearings on a nominee.
Mr Barr has voiced disapproval over some aspects of the inquiry but his views on the investigation's legitimacy remain unknown.
He was my first choice from day one.
"To the extent it is not pursuing these matters, the department is abdicating its responsibility", he was quoted in a November 14, 2017 article.
Barr wrote in a May 2017 op-ed that Trump was right to fire FBI Director James Comey, asserting that the former director "crossed a line" in the investigation of former Secretary of State Hillary Clinton.
Senate Democrats have sued the administration over the appointment, arguing it wasn't constitutional.
Barr added that he "would have liked to see him have more balance on this group". "(Barr) may be the kind of person who would be easier to confirm". But some inside the White House were concerned that Barr was too aligned with establishment GOP forces. Barr was one tough lawyer.
Senator John Cornyn of Texas, the No 2 Republican leader, agreed.