It is unclear whether she has accepted his offer concerning the position, now held by Nikki Haley, who said she would leave by the end of the year.
But when asked about Nauert later Thursday, President Trump said while she is "under very serious consideration," he had not yet made a final decision and wouldn't until next week."
"She's been a supporter for a long time, and she's really excellent," he said of Nauert.
Nauert has been the department spokesperson since April 2017 after a career as a broadcast journalist at ABC News and an anchor at Fox News. After Secretary of State Rex Tillerson was fired, she was promoted to acting under secretary of state for Public Diplomacy and Public Affairs.
Nauert met President Trump at the White House on Monday, two sources told ABC News -- her second meeting with the president about the role.
The role requires Senate confirmation.