Ms Nauert worked for Fox News from 1998 to 2005 and, after two years away during which she worked for ABC, she returned to Fox in 2007, later becoming a presenter for Fox & Friends.
While the senator acknowledged that Nauert does have State Department experience, he pointed out that "she has no experience as a diplomat", also arguing that she beings to the table "no meaningful experience in the government".
A representative of the State Department did not immediately respond to a request for comment.
Back in October, Nauert, a former Fox News host, was believed to be a "leading contender" for the position, sources familiar with the selection process said at the time.
According to multiple sources, the president will bring Heather Nauert from her current position as State Department spokeswoman to replace Haley at the United Nations. She does not have prior political or policy-making experience.
Trump expected to pick State spokeswoman for UN ambassador
It was reported in November that Nauert had been offered the job, but it was not clear at the time whether she had accepted.
President Trump said she had done "an incredible job".
Haley has also pushed a hardline against the machinations of Russian Federation President Vladimir Putin, something that many saw as contrary to the less critical statements from President Trump.
The president has reportedly sought out someone who will demonstrate loyalty.
Nauert will probably be pressed on her qualifications by Senate Democrats and could face a contentious confirmation hearing, but needs only a simple majority vote to be elevated to the role.