President Trump is expected send a tweet on Friday morning about choosing Ms Nauert to replace outgoing UN Ambassador Nikki Haley, who announced her resignation in October.
A representative of the State Department did not immediately respond to a request for comment.
Ms Haley has held the post since the beginning of Mr Trump's administration and said she would stay in the job through the end of the year.
At the time, Ms Haley described her time in the position as a "blessing," but offered no reason for leaving except a belief that government officials must know "when it’s time to step aside."
In her resignation letter, she also dismissed the possibility of running in the 2020 election.
Nauert, whose nomination would require Senate confirmation, is a former Fox News Channel correspondent and anchor.
The does not have prior political or policy-making experience, but has worked for two secretaries of state - Rex Tillerson, the current incumbent Mike Pompeo.
Ms Nauert became the State Department spokeswoman in April 2017 and, earlier this year, was named the acting undersecretary for public diplomacy and public affairs.
ABC News reported in November that Ms Nauert had been offered the job, but it was not clear at the time whether she had accepted.