Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) reportedly once suggested that President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE encourage the Chinese government to assassinate North Korean leader Kim Jong Un and replace him with a general that China could control.

Graham reportedly made the recommendation during a meeting in the White House with Trump's national security team in September 2017, according to an excerpt from veteran journalist Bob Woodward’s book, “Fear: Trump in the White House,” as first reported by the Daily Beast.

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The news outlet said that, according to Woodward, the meeting on North Korea included Defense Secretary James Mattis James Norman MattisBiden courts veterans amid fallout from Trump military controversies Trump says he wanted to take out Syria's Assad but Mattis opposed it Gary Cohn: 'I haven't made up my mind' on vote for president in November MORE and then-national security adviser H.R. McMaster and occurred shortly after Trump called Kim "little rocket man" last fall.

Trump never acted on the alleged recommendation from Graham.

A spokesman for Graham, Kevin Bishop, declined to comment on the book excerpt to The Hill. But Bishop acknowledged to the Daily Beast that Graham has tried to persuade Trump to take a more hawkish approach to foreign policy.

The Daily Beast noted that this wasn’t the only conversation between Graham and Trump about North Korea included in Woodward’s book.

In a different private conversation late last year, Trump reportedly told Graham he was open to starting a war with Pyongyang.

“There is a military option: to destroy North Korea’s nuclear program and North Korea itself … If thousands die, they’re going to die over there. They’re not going to die over here—and [Trump has] told me that to my face,” Graham said, according to the book.

But Woodward reported that Trump’s military advisers pushed back against the idea and that Marine Gen. Joseph Dunford, the chairman of the joint chiefs of staff, told Graham in February that intelligence on North Korea was too suspect to strike.

Graham “sensed that Dunford was stalling Trump’s request given the risk,” according to Woodward’s book.

The anecdotes about Graham are one of many revelations about the Trump administration included in Woodward’s new book, which was released on Tuesday. The book paints a portrait of a White House increasingly at odds with the president’s decisions.

The White House and Trump and have pushed back hard against the book's credibility, with press secretary Sarah Huckabee Sanders saying the book is full of fabricated stories.

The claim about Graham comes just a day after the White House said that planning is underway for a second summit between Trump and Kim. The leaders met over the summer in Singapore, resulting in a promise from Kim that North Korea would denuclearize in exchange for sanctions relief from the U.S.

-Updated 3:10 p.m.