Treasury Secretary Steven Mnuchin is one of the advisors to President Donald Trump under consideration to be the next White House chief of staff, according to two people with direct knowledge of the matter.

Yet Mnuchin has indicated to his inner circle that he feels best served as the head of Treasury, according to these people, who spoke on the condition of anonymity due to the privacy of the ongoing discussions.

Even so, according to a source close to the Treasury secretary, some of Trump's family members are pushing for Mnuchin as a possible replacement for the departing John Kelly, who is set to leave the administration by the end of the year after an often-chaotic time in the job.

It's unclear whether Trump himself has spoken with Mnuchin about becoming his next chief of staff. There are other names being mentioned in reports as potential replacements for Kelly, but it's not clear whether any of them are in position to take the role.

Mnuchin, a former Goldman Sachs executive, is one of the members of the administration who is considered to be more in favor of free trade, as opposed to hawks such as trade advisor Peter Navarro. Mnuchin's potential move to chief of staff would come amid crucial trade talks with China. Markets, however, could see Mnuchin's move away from Treasury as a potentially destabilizing action.

The New York Times had reported that Mnuchin was a possible contender for the chief of staff job.

Mnuchin's spokesman declined to comment. White House press secretary Sarah Huckabee Sanders did not respond to requests for comment.

White House budget chief Mick Mulvaney and U.S. Trade Representative Robert Lighthizer, the president's chief trade negotiator, are also reportedly on the short list.

Lighthizer had said in an interview with CBS' "Face the Nation" on Sunday that he had not been asked to replace Kelly.

On Sunday, Nick Ayers, the chief of staff to Vice President Mike Pence who had been the favorite to replace Kelly, announced he would be departing the administration at the end of the year.

People close to Ayers said he could go back to leading Pence's political action committee, the Great America Committee.

Kelly, who had a tumultuous tenure since taking over the role in summer 2017, had committed to staying through the 2020 election.