Requests for comment to the state department and the White House were not immediately returned.
Early in her career, Nauert worked as a health insurance consultant, according to the State Department, which says she studied at Mount Vernon Seminary and College, a private women's college in Washington DC, and Columbia University's journalism school.
During Pompeo's tenure, she has been able to travel on official trips - something Tillerson blocked her from doing - and rose to temporarily hold the position of acting under secretary for public diplomacy and public affairs.
Ms Nauert, whose nomination would require Senate confirmation, is a former Fox News Channel correspondent and anchor.
Numerous reports in the United States media - the first of which appeared in Bloomberg news - said Nauert would be nominated Friday, citing sources close to the matter.
Trump told reporters in November that Nauert, who does not have any prior political or policy-making experience, was "under very serious consideration" for the position. Haley, former governor of the USA state of SC, said she did not know what she would do next, but clarified that she would campaign for Trump ahead of the 2020 presidential election.
Nauert joined the State Department in April 2017.
Six missing after US military aircraft crashes off Japan
The US has more than 50,000 troops stationed in Japan, more than 18,000 of them in the US Marine Corps . The aircrafts had launched from Marine Corps Air Station Iwakuni, a USA station in Japan .
Trump has been known to change course on staffing decisions in the past.
Her appointment to the United Nations role would have to be approved by the US Senate.
Nauert, left, and White House press secretary Sarah Sanders.
A key question with Nauert will be whether the president keeps the United Nations envoy job as a Cabinet-level position, or downgrades it to report through Pompeo, as other administrations have sometimes done.
Ms Nauert is said to be good friends with Ivanka Trump and her husband, Jared Kushner.
Although some have speculated that Haley may challenge Mr. Trump in 2020, Haley has said that she will support the president.