She would replace Nikki Haley, who was twice elected governor of SC but also lacked foreign policy experience.
"It will have to do with the joint chiefs of staff, the succession", he told reporters outside the White House, suggesting he may name a new top USA military officer.
Nauert went on to graduate from Mount Vernon College in Washington and Columbia University's Graduate School of Journalism, according to her bio on the State Department website.
Nauert needs a simple majority to be named the ambassador and will be questioned by Democrats in the Senate.
Nauert will face a full plate at the United Nations, with Iran and North Korea and other issues dominating the US agenda there.
After her appointment as acting undersecretary, she was for a time the highest-ranking woman and fourth highest-ranking official at State.
Trump told reporters that Nauert, who is in line to take over from Nikki Haley, had proven herself as a "very talented, very smart" member of his administration.
Nauert covered domestic and global stories as an ABC News correspondent from 2005 to 2007 prior to joining Fox.
Haley also dismissed the possibility of running for president in 2020, saying she will support Trump's re-election campaign. She is a quick study.
Early praise for the appointment came from Israel, which has long counted on the United States to veto unfriendly resolutions on the UN Security Council.
White House press secretary Sarah Huckabee Sanders described Nauert in March as "a team player" and "a strong asset for the administration". In turn, these played a role in weakening North Korea's weapons program, and persuading Kim Jong Un to take part in negotiations, she said.
"Heather Nauert will be nominated for the ambassador to the United Nations", Trump told reporters on his way to Marine One on Friday.
According to Daniel Benjamin, a state department counterterrorism coordinator during the Barack Obama administration, Nauert's appointment shows that Trump and his top officials are looking to firmly control U.S. foreign policy.
However, Haley admitted she and the president "agree on most things", but "there are certainly things that we don't agree on". That means Nauert could be overshadowed by Pompeo or Trump's national security adviser, John Bolton, who had the United Nations job in 2005 and 2006. And that's the point: Trump values how his messages and policy decisions are explained by his subordinates, and has said his instincts and intellect are better than most.
Nauert became an anchor on Fox & Friends, Trump's favourite television talkshow, where she helped air the network's recurrent themes about the threat of immigration, warning that immigrant children arriving in the U.S. could be bringing disease into the country, and that Sharia law was spreading in urban areas with Muslim populations. "Haley has done representing your administration and the American people".