Barr, if nominated by Trump and confirmed by the Senate, would replace Acting Attorney General Matthew Whitaker, who has been filling the position since Sessions was ousted on November 7. With the current session of Congress set to soon end, anyone Trump nominates may have to wait until well into 2019 for confirmation.
Barr was attorney general between 1991 and 1993, serving in the Justice Department at the same Mueller oversaw the department's criminal division. He was promoted to deputy attorney general next, and then to the top role.
Democrats would presumably want reassurances that Barr, who as attorney general would be in position to oversee Mueller's investigation, would not do anything to interfere with the probe.
Senate Majority Whip John Cornyn, a Texas Republican who sits on the Judiciary Committee, called Barr an "interesting pick".
At the Justice Department, Barr's work ranged from combatting violent crime to investigation the Pan Am 103 bombing.
Trump heavily derided Mueller's team earlier this year for being comprised of many registered Democrats and Democratic donors.
He also told the New York Times that there was justification for further investigation of Clinton's role in approving the Uranium One sale to the Russians.
He also says Barr was his "first choice from Day One".
"To the extent it is not pursuing these matters, the department is abdicating its responsibility", he said.
Barr has been on a White House short list of contenders for several weeks, said a person with knowledge of internal discussions who was not authorized to speak publicly. He expressed confidence in Mueller early on and suggested the investigation wouldn't devolve into a "witch hunt", but he also has shared some disappointment when asked by The Washington Post past year about the donations that some of Mueller's team members made to Democrats. Barr was one tough lawyer. "I am concerned he has said some negative things about the Special Counsel's office and some of the prosecutors he had in place", Democratic Senator Amy Klobuchar told MSNBC on Thursday after Barr's name surfaced. I was happy that GTE's conduct of the litigation was considerably more aggressive than that of other similarly situated carriers who were also required to share their facilities and equipment with new competitors under the Act.