Haley unexpectedly announced her resignation in October and promised to serve in her role through the end of 2018.
Trump is expected to tweet the announcement Friday morning, according to Fox News.
"I expect to continue to speak out from time to time on important public policy matters, but I will surely not be a candidate for any office in 2020", she said.
Trump told reporters last month that Nauert was "excellent", adding, "She's been a supporter for a long time".
Trump had previously said Nauert was under serious consideration to replace Haley, though he's been known to change course on staffing in the past.
Twitter Outraged Over Article Labelling Priyanka Chopra 'Global Scam Artist'
Meanwhile, Nick's brother, Joe Jonas , couldn't help but gush over the newlyweds via Twitter . It's not even in my stratosphere. It reeks of envy and bitterness.
- With files from the Associated Press.
The state department has made no comment.
The current State Department spokeswoman has earned the trust of Secretary of State Mike Pompeo, and Trump's daughter Ivanka Trump and her husband Jared Kushner, Bloomberg reported. Nauert was then appointed acting undersecretary of state for public diplomacy and public affairs and was for a time the highest-ranking woman and fourth highest-ranking official in the building.
ABC News reported in November that Nauert had been offered the United Nations job, but it was not clear at the time whether she had accepted.
Ahead of the vote, the U.S. ambassador sent a letter to all UN missions to make clear that "the United States takes the outcome of this vote very seriously".
The post is considered one of the highest profile positions in US diplomacy. She does not have prior political or policy-making experience. All the while, she stayed in the good graces of the White House, even as Tillerson was increasingly on the outs.