The announcement is expected to come on Friday, two officials say.
Haley announced in October she would be leaving the job by the end of the year.
The former Fox News host's precipitous rise since arriving at the State Department in 2017 sets the stage for a potentially tough Senate confirmation hearing, where Democrats will likely grill Nauert on her qualifications for the position.
Nauert covered domestic and global stories as an ABC News correspondent from 2005 to 2007 prior to joining Fox.
After Tillerson's departure, Nauert was catapulted into the position of acting undersecretary of state for public diplomacy and public affairs. With Mike Pompeo in charge of State, Nauert has been on the road much more.
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Nauert will face a full plate at the United Nations, with Iran and North Korea and other issues dominating the USA agenda there. If confirmed by the Senate, she would be a leading administration voice on Trump's foreign policy.
At the UN, Nauert is seen as a cipher. He said he thought she would be "respected by all".
Democratic senators likely will resist her nomination, but lack the votes to block it. Nauert won't be going to NY to shape America's foreign policy.
Haley similarly had little foreign policy experience when appointed, although she had a national name as the governor of SC.
If Nauert is confirmed for the job, it would cap a precipitous rise in diplomacy in less than two years. She primarily worked as a health insurance consultant in Washington, D.C., and became a spokeswoman for the State Department in April 2017.
Maybe the new ambassador will eventually become a rock star beyond the ranks of Fox News viewers and enhance her own power, so long as she doesn't undercut the ultimate Boss. He noted that "people were slightly denigrating about Haley too, because of her relative lack of experience and the general view is that she did quite well". But when White House officials told her they wanted her, she accepted.
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Danny Danon, the Israeli ambassador to the United Nations, swiftly welcomed Nauert's appointment.
"It will have to do with the joint chiefs of staff, the succession", he told reporters outside the White House, suggesting he may name a new top USA military officer. And that's the point: Trump values how his messages and policy decisions are explained by his subordinates, and has said his instincts and intellect are better than most.
Republicans, who control the Senate, said Barr was well qualified. "Grenell is known to be hard to work with". "For Nauert it is going to be more about implementing than developing policies".
Asked about Israel's plans to demolish the Palestinian village of Khan al-Ahmar, in spite of protests from the European Union and U.S. lawmakers, Nauert framed the issue as an Israeli legal matter, referring the reporter who posed the question to the Israeli government.
Nonetheless, during her two-year stint, Haley became a darling of the Trump administration and the pro-Israel community for her vociferous defense of the Jewish state at the United Nations, a body often seen as hostile to Israel.
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