(CNN) Several of President Donald Trump's outside advisers have told him over the past week he requires neither a chief of staff nor a communications director, at least in the traditional definition of those jobs, according to a person familiar with the conversations.

Trump has absorbed the advice, but offered little indication whether he's interested in taking it, the person said. He's been warned by other confidants that it's impossible to run the West Wing without a chief of staff.

There are no signs Trump is ready to dismiss top aide John Kelly. But the option of running his White House without a chief of staff has been planted in Trump's mind, and he's not rejected it outright, the person said.

Trump has expressed frustration at the management structure in the West Wing, believing it doesn't suit the freewheeling style he employed as a businessman. And he's persistently annoyed by headlines and television coverage of his presidency. After a year in office, he's more willing to change long-established West Wing structures, people familiar with his thinking say.

He's begun working around Kelly on a number of fronts, including during some phone calls with foreign leaders, on certain policymaking decisions, and in executing some of the past month's staffing changes, people familiar with the matter said. Kelly, meanwhile, has sought to bring further order to the policymaking process, including by naming Chris Liddell as his deputy for policy implementation.

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