(CNN) Elliott Abrams, a neoconservative Republican insider, is emerging as President Donald Trump's choice be Deputy Secretary of State -- a pick that could test Trump's willingness to work with members of a foreign policy establishment that didn't back him during the campaign, according to sources familiar with the situation.

Trump will meet Tuesday with Abrams, who served under Presidents Ronald Reagan and George W. Bush. Secretary of State Rex Tillerson, who has met with Abrams and wants him for the job, also will attend the meeting.

The deputy at the State Department is a key post that holds considerable influence and responsibility in running the department.

As a former CEO of Exxon Mobil, Tillerson comes to the job having relationships with many world leaders, while Abrams is a well-respected, albeit controversial, foreign policy insider with considerable government experience. Several State Department officials believe he would complement Tillerson.

His appointment has been on hold for weeks as Trump's senior advisers, led by White House chief strategist Steve Bannon, debated whether Abrams, someone from the foreign policy elite, could be trusted.

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