Washington (CNN) William "Bill" Barr, a former attorney general under President George H.W. Bush, is emerging as a consensus candidate to succeed Jeff Sessions as attorney general, two sources familiar with President Donald Trump's thinking tell CNN.

A third source familiar with the process said if Trump offered the position to Barr, he would be willing to accept.

Trump's consideration of a new attorney general comes during a critical time for special counsel Robert Mueller's investigation, of which the next Justice Department chief will inherit oversight. Barr, 68, has previously offered mixed opinions about the investigation, having praised Mueller but also publicly criticizing political donations made by several members of his team.

The Washington Post first reported that Barr is the leading candidate. Sources cautioned to CNN, however, that Trump makes the final decision.

Barr served as Mueller's boss when he was attorney general in the early 1990s and Mueller led the criminal division at the Justice Department.

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