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.
It is not yet clear who would take over her role as State Department Spokesperson.
Trump will send a tweet on Friday morning about choosing Nauert to replace the outgoing United Nations ambassador, Nikki Haley, who announced her resignation in October, Fox News reported, citing multiple sources.
Having the direct support of the president and Secretary of State, Mike Pompeo, could buttress her image, however, among global diplomats at the United Nations, who have bristled at Donald Trump's "America First" foreign policy.
Trump expected to pick State spokeswoman for UN ambassador
Nauert became the state department spokeswoman in April 2017 and this year was named the acting undersecretary for public diplomacy and public affairs.
Three people familiar with President Trump's decision to name Nauert confirmed the pick, according to the report. The officials were not authorized to speak publicly before Trump's announcement.
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.
Nauert would take up the USA mantle at the United Nations including holding sanctions on North Korea and defending Israel.
White House press secretary Sarah Huckabee Sanders described Nauert in March as "a team player" and "a strong asset for the administration". Trump is a regular viewer and one time guest of the show, and Nauert herself has developed a close relationship with Trump's daughter Ivanka. "What we've really discovered over the last two years is that even when you have a relatively mainstream, relatively collegial, relatively influential ambassador to the United Nations like Haley, that only buys you a limited degree of protection from a president like Trump".
Xi, Trump agree to ease trade tensions
Other attendees on the U.S. side included Treasury Secretary Steven Mnuchin , Secretary of State Michael Pompeo, U.S. The White House announced it would hold fire on raising tariffs on $200bn (£156bn) worth of goods from China.