WASHINGTON — In the midst of a Cabinet shake-up and a possible staff upheaval, President Donald Trump considered firing his chief of staff this month and not naming a successor, according to three people familiar with the discussions. Trump has mused to close associates about running the West Wing as he did his business empire, essentially serving as his own chief of staff, these people said.

In conversations with allies outside the White House, the president envisioned a scenario in which a handful of top aides would report directly to him — bypassing the traditional gatekeeper position. The president hasn't publicly discussed his deliberations.

Trump, who is said to always be reimagining his staff positions, appears to have tabled the suggestion for now. His second chief of staff, John Kelly, remains in his role after intense speculation about his job security. But the president was intrigued by, and seriously considered, the idea of not replacing him had he left.

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Trump liked the idea particularly because it would be more in line with how the former CEO conducted business in the private sector: with a more open-door policy that allowed him unfettered access to outsiders and fewer roadblocks to decision making. And he has privately pointed to precedent in the presidencies of Lyndon Johnson, John F. Kennedy and Jimmy Carter, people familiar with the discussions said.

Some allies grumbled about the feasibility of removing what in past administrations had been a critical position charged with managing the operations of staff in the White House, as well as the information flow, decision-making process and access to the president.

But several sources close to the administration argued it wouldn’t be such a departure from the current status: “Donald Trump is the chief of staff. He already calls the shots,” said one.

The president’s former chief strategist, Steve Bannon, raised the prospect Thursday at a Financial Times forum, suggesting the president should become his own chief of staff if Kelly ever departed.

“I’ve actually argued that if General Kelly at any time does decide to leave — (or) the president decides it’s time for him to move on — I don’t believe there will be another chief of staff,” Bannon said. “I think there will be five or six direct reports like there was in Trump Tower.”

Chris Whipple, author of “The Gatekeeper” about White House chiefs of staff, said the idea is ill-advised.

“History is littered with the wreckage of presidencies that have tried to do this, and Jimmy Carter is the perfect example of why it’s a nonstarter,” said Whipple, who explained that some presidents tried to institute “spokes-of-the-wheel” models of leadership inside the West Wing, with the commander in chief at the center.

It rarely worked, he said.

“The overarching thing that I learned from studying five decades of this is that every president learns, often the hard way, that you cannot govern effectively without empowering a chief of staff as a first among equals to execute your agenda — and most importantly, tell you what you don’t want to hear.”

“If Trump is taking the opposite lesson," Whipple said, "that way lies disaster for him.”