WASHINGTON (REUTERS) - President Donald Trump is considering Republican Representative Mark Meadows, former campaign adviser David Bossie, and former New Jersey Governor Chris Christie for White House chief of staff, a source familiar with the search said on Monday (Dec 10).

Another source said Trump was also looking at US Trade Representative Robert Lighthizer for the job.

The search comes after the president's initial choice for the job, Nick Ayers, bowed out on Sunday and as the White House braces for an onslaught of political and legal challenges in the coming year.

On Saturday, Trump said his current chief of staff, retired General John Kelly, would be leaving the White House at the end of the year. The two men had clashed for months.

Ayers, who is Vice President Mike Pence's chief of staff, had agreed to come on for an interim period but declined to commit to stay for the remaining two years of Trump's term.

The new chief of staff will have to navigate a challenging political environment as Trump begins his third year in office and prepares for a 2020 re-election campaign.

Democrats take control of the House of Representatives in January, and US prosecutors are intensifying their probe into potential collusion between Trump's 2016 presidential campaign and Russia.

Trump has denied any collusion, while calling the probe a "witch hunt".

A White House official said Trump was considering four people for the position, but declined to give names.

Other names that have come up for the job include Treasury Secretary Steven Mnuchin, but a person familiar with Mnuchin's thinking said he believed he could serve better in his current position.

White House budget director Mick Mulvaney is no longer interested in the job, said a source close to him, adding he would prefer to serve at the Department of Commerce or Treasury "if that's where the president needed him". Neither of those Cabinet-level secretary jobs is open at the moment.

Lighthizer has gained prominence in the administration for his handling of trade negotiations. He is the point person for talks between the administration and China over trade, an issue likely to dominate the first part of 2019 and beyond.

"The argument for Lighthizer is he'll be able to navigate trade negotiations - which could be a defining part of the presidency, and has run a major company," said one official familiar with the process.

"The argument for Meadows is (Trump) ultimately wants a political strategist going into 2020 - which Mark is."

Meadows said in an interview with Fox News Channel that he had not had a conversation with Trump about the opening since Ayers declined the offer, but added that serving as chief of staff was an honour and he was "favourably inclined to at least have a discussion with the president".

Trump is expected to make a decision about the position by the end of the year.