Haley is the first Indian-American to ever appointed to a Cabinet position in any US presidential administration.
Nauert had been the favourite after Haley, 46, announced that she would leave the job.
Trump is expected to make the announcement on Friday, the reports said.
If confirmed, Nauert, a former Fox News anchor who has served as the public face of the State Department since last year, would be one of the most prominent promoters of Trump's 'America First' foreign policy.
Although some have speculated that Haley may challenge Trump in the 2020 presidential election, Haley has said that she will support the president.
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