Story highlights Bannon is on leave as executive chairman of Breitbart News

RNC chairman Reince Priebus is also in the running for the key White House post

Washington (CNN) President-elect Donald Trump is strongly considering naming his campaign CEO Steve Bannon to serve as his White House chief of staff, a source with knowledge of the situation told CNN on Thursday.

The White House chief of staff is typically tasked in large part with ensuring that all wheels are spinning in the complex White House organization, and the source said that some people in Trump's orbit do not think Bannon, the executive chairman of Breitbart News who joined Trump's campaign in August, is the best fit for that position.

Trump's contemplation of Bannon as chief of staff comes as his presidential transition team is feverishly ramping up its efforts to build out an administration after his surprising win Tuesday.

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It also highlights how Trump is contending with competing impulses as to whether he should fill the ranks of his White House with the right-wing figures who energized his campaign or more establishment figures experienced in the ways of Washington.

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