US Treasury Secretary Steven Mnuchin and Republican Representative Mark Meadows are among possible contenders to replace current White House Chief of Staff John Kelly, Reuters reported, citing sources.
On Sunday, the US president said that a decision would be made soon.
The White House chief of staff responded "to a narrow set of questions" from investigators on charges of obstruction of justice. The White House earlier this summer objected to the request from Mueller's team for an interview with Kelly.
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Media reports suggested that Vice President Mike Pence’s Chief of Staff Nick Ayers was originally Trump's top pick for the post, but a disavowal of the offer by Ayers has again thrown the matter open.
Meanwhile, Nick Ayers, the 36-year-old chief of staff to the Vice President, tweeted Sunday that he "will be departing at the end of the year but will work with the #MAGA team to advance the cause," referring to Trump's campaign.