Former Fox News anchor and State Department spokeswoman Heather Nauert has withdrawn from consideration to be the US ambassador to the United Nations amid criticism that she lacked the gravitas for one of the top diplomatic posts.

"The past two months have been gruelling for my family and therefore it is in the best interest of my family that I withdraw," Nauert said in a statement.

The announcement came after weeks of often mocking criticism over President Donald Trump's nomination of Nauert, who had no foreign policy experience until two years ago when she was named State Department spokeswoman.

Leading Democrats questioned whether Nauert, despite her poise at the podium, had the skills to negotiate on complex international issues or go head-to-head with seasoned diplomats from adversaries such as Russia.

But with Trump's Republican Party in control of the Senate, her nomination did not seem to be in serious jeopardy, raising questions on why she announced her withdrawal abruptly in the evening on a holiday weekend.

Bloomberg News, quoting anonymous sources, said that a White House background check had discovered that Nauert employed a nanny who was legally in the United States but not authorised to work.

Trump, whose tough line on immigration is his signature issue, started looking yesterday for a new nominee, the report said.

Trump, an avid viewer of conservative-leaning Fox News where Nauert was once an anchor on morning show "Fox and Friends," told reporters in December that he wanted her as UN ambassador.

Her nomination, however, was never formally submitted to the Senate and she has vanished for over two months as she prepared for a confirmation hearing - and, eventually, the job.

The UN post has been vacant since the start of the year after Nikki Haley, a former South Carolina governor and rising star in Republican politics, decided to leave.