The Wall Street Journal's Michael Bender makes the claim in his new book, Frankly, We Did Win This Election: The Inside Story of How Trump Lost.
According to Bender, the former president called a meeting where he tasked his high-ranking officials to find the leaker.
"Trump boiled over about the bunker story as soon as they arrived and shouted at them to smoke out whoever had leaked it. It was the most upset some aides had ever seen the president," Bender writes.
During the tense meeting, Mr Trump reportedly called for the leaker to be put to death.
"Whoever did that, they should be charged with treason!" Mr Trump is reported to have said. "They should be executed!"
Mark Meadows, the White House Chief of Staff, reportedly tried to calm Mr Trump, assuring him they would seek out the leaker.
"I'm on it. We're going to find out who did it," Mr Meadows is reported to have said.
Bender describes the former president's staff as being nervous and avoiding eye contact with Mr Trump during the tirade.
Finding the leaker apparently became an obsession for Mr Trump in the days following the incident. Bender writes that the then-president repeatedly asked Mr Meadows if there had been any success finding the individual who leaked the information.
At the time, Mr Trump tried to downplay his retreat to the bunker by claiming he was "inspecting" it, which is not a task that would normally fall to the President of the United States.
Social media users predictably blew up at the revelation, with one describing the former president's reaction as something "crazy dictators do."
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