Plucked from Fox by the White House to serve as State Department spokeswoman, Ms Nauert catapulted into the upper echelons of the agency's hierarchy when Mr Tillerson was sacked in March and replaced with Mike Pompeo.
The D-Day invasion was carried out by the United States and its allies.
William Barr, 68, who was attorney-general under President George HW Bush, is lined up to return to the role.
Mr. Barr, now a lawyer at the firm Kirkland & Ellis, has worked as a lawyer for high profile firms, including at telecom company Verizon. But since Republicans will continue to hold a majority in the Senate when the new Congress convenes in January, experts say she is likely to be confirmed.
Mr. Barr is a proponent of extensive presidential powers.
"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".
Ms Haley has served almost two years in the post.
Ninety percent of her job will be done if she only stands tall in the face of all the globalized hand-wringers of the world - if she only, for instance, does what outgoing Ambassador Nikki Haley has done, what former Ambassador John Bolton once did. According to The Associated Press, Nauert's relationship with former Secretary of State Rex Tillerson was strained. She'll be Ambassador to the United Nations.
Trump told reporters last month the former Fox News anchor was "under very serious consideration".
Much of the initial reaction to Nauert's appointment concerned itself with her extremely limited foreign policy background, and the possibility that her main credential was her experience as anchor on Trump's very favorite television show, Fox & Friends.
The State Department declined to comment and Nauert did not immediately respond to a request for comment.
Ms. Nauert's profile became more visible after Mr. Tillerson was sacked in March. She became the State Department's spokeswoman in April 2017 and was named earlier this year as the acting undersecretary for public diplomacy and public affairs. If confirmed by the Senate, she would be a leading administration voice on Trump's foreign policy.
However Ms Haley has made no secret of the fact that she has had policy disagreements with Mr Trump.
However, Haley admitted she and the president "agree on most things", but "there are certainly things that we don't agree on". "Traditionally. we've either had people with a lot of experience in global affairs and /or a lot of experience as academics", he said.
Sen. Jeff Merkley of OR, the top Democrat on a Senate subcommittee that oversees America's relationship with the United Nations, slammed Trump's nomination of Nauert.