On Friday, Trump revealed Haley's replacement at the worldwide body, confirming that he intends to appoint US State Department spokeswoman Heather Nauert, a former Fox News correspondent, to the position.
Sessions stepped down amid criticism from Trump and was replaced on an interim basis by his Chief of Staff, Matthew Whitaker.
Barr would also investigate the alleged investigation on Trump's campaign plot with Russian Federation over controlling the 2016 USA general election. Remarkably, Barr used to be a colleague of Mueller at the Justice Department, so Barr should know firsthand that Mueller is trustworthy and not the boogeyman the president claims. Barr is the one who, under Bush's presidency, had "provided legal reasoning used by the administration to justify the invasion of Panama and the arrest of Manuel Antonio Noriega".
Barr, 68, served as first deputy attorney general and then as attorney general from 1989 to 1993 under the late President George H.W. Bush.
Nauert, whose nomination would require Senate confirmation, is a former Fox News Channel correspondent and anchor.
"If I were the State Department's spokesperson, on an official trip to learn more about the dark, dubious circumstances surrounding the disappearance of a USA resident, I probably would have skipped the tourist-in-Riyadh photos".
"People in this Iran-Contra matter have been prosecuted for the kind of crimes that would not have been criminal or prosecutable by the Department of Justice, applying standards that we have applied for decades to every citizen", Walsh quoted from a December 1992 interview Barr gave.
Mr. Barr, now a lawyer at the firm Kirkland & Ellis, has worked as a lawyer for high profile firms, including at telecom company Verizon.
"To the extent it is not pursuing these matters, the department is abdicating its responsibility", Barr said.
He also wrote an op-ed for The Washington Post in May 2017 defending Trump's decision to fire former FBI Director James Comey, one of the actions Mueller has been examining for possible obstruction of justice.
He has raised concerns about Mr Mueller's appointment of prosecutors with a history of donating to Democratic candidates, saying he "would have liked to see him have more balance on this group". Secretary Pompeo appointed her as Acting Undersecretary of State for Public Affairs and Public Diplomacy in April this year and she has accompanied Mr. Pompeo on foreign trips, most recently to Brussels on December 3 for a North Atlantic Treaty Organisation meeting of Foreign Ministers and meetings with the Belgian administration as Belgium takes a seat at the UN Security Council.
Democrats are promising aggressive oversight of Trump's administration and business activities when they take control of the US House of Representatives in January following their gains in last month's elections.