(CNN) Almost two months after President Donald Trump said he would quickly name a replacement for Nikki Haley, he is still struggling to pick his next ambassador to the United Nations.

At first, former deputy national security adviser to the President Dina Powell was under consideration, then took herself out of contention. Then a long list of candidates were floated including Kay Bailey Hutchison, the ambassador to NATO; Nancy Brinker, founder of the Susan G. Komen organization; Richard Grenell, the ambassador to Germany; and John James, who recently lost a Michigan Senate race to Democrat Debbie Stabenow.

But in late October Trump seemed to have found his favorite and told aides he wanted State Department spokeswoman Heather Nauert , a former Fox News host. Trump went public and said Nauert was "excellent," noting she's "been a supporter for a long time. And she's really excellent."

But after CNN and multiple other outlets reported that Trump was telling others Nauert was his top choice, her critics launched an intense lobbying effort to squash Nauert's candidacy. A source with knowledge of the process, said top advisers pushed back and asked the President to delay an announcement and consider other candidates because they were concerned that Nauert did not have enough foreign policy experience. They argued that her precipitous rise since arriving at the State Department in 2017 would set the stage for a tough Senate confirmation hearing, where Democrats would likely grill Nauert on her qualifications.

For the last month, advisers have floated other candidates, but so far none of them seem to have impressed Trump and several officials say he has remained high on Nauert. They say her lack of experience matters less to the President, an avid fan of Fox News, than her loyalty to the White House. The fact that she's a woman and could be a polished proxy on television appeals to Trump, according to sources familiar with his thinking.

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