Ms Nauert, a former Fox News presenter, has been spokeswomen for the US Department of Defence since last year. Trump met Ms Nauert in the Oval Office on Monday, but a job offer has not been officially confirmed. She also served as Acting Under Secretary of State for Public Diplomacy and Public Affairs between March and October 2017.
If confirmed, Ms Nauert’s appointment could prove controversial given her apparent lack of foreign policy experience.
She will need to win Senate confirmation to assume the role.
It remains to be seen whether the UN envoy position will remain Cabinet level.
There had been discussions about downgrading the role, so the UN envoy would report directly to Secretary of State Mike Pompeo.
READ MORE: Donald Trump: Is Donald Trump spending Christmas in the White House?
Trump had reportedly also been considering ex-White House aide Dina Powell, US Ambassador to Germany Ric Grenell, and US Canada Ambassador Kelly Croft for the job.
Ms Nauert started her career as a reporter for CBS News, before co-hosting Fox News morning show “Fox & Friends”, of which President Trump is known to be a frequent viewer.
Ms Powell, Trump former deputy national security advisor, was reportedly the frontrunner before she dropped out last month.
Trump also commented that his daughter Ivanka would be “incredible” in the role, but noted her appointment would lead to accusations of nepotism.
Ms Nauert is known to be personally close to both Ivanka Trump and her husband, Jared Kushner, who are both White House advisors.
If successful Ms Nauert will replace Nikki Haley who announced her resignation at the end of October.
Ms Haley said she was taking a break after two terms as South Carolina governor and two years at the UN.
However, Ms Haley insists she remains supportive of Trump and will back his reelection campaign in 2020.