Barr previously served as attorney general under President George H.W. Bush.
On paper William Barr looks like a safe pick for U.S. attorney general.
Barr has worked in the private sector since serving as attorney general from 1991 to 1993, retiring from Verizon Communications (VZ.N) in 2008.
Democrats won't be encouraged to learn that he expressed support for Donald Trump's firing of FBI Director James Comey and recommended further investigation of Democrat Hillary Clinton.
In a 2017 interview with The Washington Post, Barr had a critique for Special Counsel Robert Mueller, who is spearheading the Russian Federation investigation. He is now an attorney for Washington, DC law firm Kirkland and Ellis.
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Barr also wrote past year that the administration's decision to fire James B. Comey as FBI director was "quite understandable" because, in his view, Comey had usurped the power of the attorney general when he publicly announced his recommendation not to charge former Secretary of State Hillary Clinton during the investigation of her private email server.
"To the extent it is not pursuing these matters, the department is abdicating its responsibility", Barr told the newspaper. "(Barr) may be the kind of person who would be easier to confirm".
Barr also said James Comey's firing was "understandable" and that he "crossed a basic line" and "transgressed" in his role as Federal Bureau of Investigation director.
Barr has been somewhat critical of special counsel Mueller's investigation into Russian meddling in the 2016 elections and has claimed there is more basis to investigate former Secretary of State Hillary Clinton for her role in approving the 2010 acquisition of US uranium stockpiles by a Russian energy company - a complicated deal that has come to be known simply as Uranium One.
He has said that Robert Mueller hired too many prosecutors with Democratic campaign ties for his investigative team - telling the Washington Post he "would have liked to see [Mueller] have more balance".
One of the people who spoke to the AP said there have been discussions among senior administration officials about Barr's willingness to do the job, and said the belief was that he was open to doing it if asked.
Senator John Cornyn of Texas, the No 2 Republican leader, agreed.