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(CNN) —  

A Trump ally’s notes visible as he visited the West Wing on Friday revealed a suggestion to replace the current CIA director with the current acting chief of staff at the Pentagon. But according to multiple sources, it was not the first time the idea was broached inside the White House.

MyPillow CEO Mike Lindell, a Republican donor who has informally advised President Donald Trump, was seen leaving the West Wing on Friday carrying pages of notes that appear to outline a series of recommendations. Among those that are visible are the words, “Move Kash Patel to CIA acting” a reference to the current chief of staff to acting Defense Secretary Christopher Miller.

Patel, who has held a number of senior jobs in the administration, was named chief of staff to Miller a few days after the general election and is widely viewed as a Trump loyalist.

Captured by a Washington Post photographer, the images sparked immediate questions about Trump’s final moves as President. But according to two administration officials, Trump has actually discussed with others the idea of installing Patel as acting CIA director before.

Trump has been on the verge of firing CIA Director Gina Haspel several times only to be pulled back from the brink, multiple sources have previously told CNN. In December, he and others concocted a plan to terminate Haspel and put Patel in charge of the CIA. Multiple options were discussed, including firing Haspel’s deputy Vaughn Bishop and replacing him with Patel, which they believed would force Haspel to quit, and also firing both and making Patel acting director.

But sources told CNN that the President had backed off from the idea after aides convinced him that firing Haspel with only weeks left in his presidency was counterproductive.

While it wasn’t immediately clear whether the President discussed the issue of CIA leadership with Lindell during his visit Friday to the White House, its mention in Lindell’s notes renewed speculation that the issue isn’t moot.

Weeks ago, Trump was considering a broader Cabinet shake-up after losing reelection, the sources said.

Miller was named to the top defense job a few days after the election. He and Patel had worked together on counterterrorism issues at the National Security Council earlier in Trump’s term.

If the idea is truly being considered still with just days to go in Trump’s term, trying to put Patel in charge of the country’s preeminent intelligence service would require an enormous amount of last-minute bureaucratic gymnastics. Current and former officials said that not only would Haspel need to be ousted but her deputy, Bishop, would need to be removed as well.

Haspel has angered some people in Trump’s orbit for stonewalling efforts by Director of National Intelligence John Ratcliffe to declassify documents related to the FBI’s Russia investigation. But even those officials who have pushed for her ouster in recent months believe the time is long past for making a move. Trump and Ratcliffe also have the authority to declassify documents themselves, so firing Haspel at this point would carry an additional tinge of spite.

Asked if there was any way Trump would make such a high-profile change with just a few days left, one senior administration official said, “Frankly, he’s running out of people who’d even know how to implement those changes. There’s no one to do the paperwork, which is pretty complicated for unorthodox personnel moves.”

Lindell confirmed to CNN’s Jim Acosta that he did meet with Trump for about five minutes on Friday and said he had tried to hand the President what he described as evidence of voter fraud. Acosta conducted a brief interview with Lindell, who did not substantiate any of his claims but merely repeated some of the same false conspiracy theories spouted by Trump since the election.

Lindell said Trump had told him to turn over his material to lawyers working at the White House, who would look into it.

Asked whether he believes Democrat Joe Biden won the presidential election, Lindell said no.

“No, he didn’t win the election, because I’ve seen it,” Lindell said.

Patel did not immediately respond to CNN’s request for comment. The CIA, the Pentagon, the White House and the National Security Council also did not immediately respond to CNN’s inquires.