Nauert's nomination had been rumoured for weeks, and she had started handing over some of her responsibilities as spokeswoman to her deputy, Robert Palladino.
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.
Plucked from Fox by the White House to serve as State Department spokeswoman, Nauert catapulted into the upper echelons of the agency's hierarchy when Tillerson was sacked in March and replaced with Mike Pompeo.
If confirmed, Nauert, 48, would succeed Nikki Haley, who said in October she would be leaving the United Nations post at the end of the year.
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Nauert was formerly a co-host on morning cable news show "Fox & Friends" as well as a correspondent for CBS News.
Nauert became the State Department spokesperson in April 2017 and, earlier this year, was named the acting undersecretary for public diplomacy and public affairs. In her first speech as ambassador, she warned that there would be consequences against those nations that worked against the will of the U.S.at the global organization. She announced in October that she would leave the position by the end of the year.
Her appointment to the United Nations role would have to be approved by the US Senate. She does not have prior political or policy-making experience.
Trump told reporters last month that Nauert was "excellent", adding, "She's been a supporter for a long time". All the while, she stayed in the good graces of the White House, even as Tillerson was increasingly on the outs.