The veteran investigative reporter warned he had "literally hundreds of hours of tapes."
The author did not comment on what he thought Trump's intent was with the comment, which has been described as an anti-Semitic dog whistle.
The book outlines how Trump told former staff secretary Rob Porter that the tweet "may be my best ever."
"China needs to kill him and replace him with a North Korean general they control," the senator apparently said.
"The cover-up is always worse than the crime, and this one is very shady," the Watergate lawyer said.
Trump allegedly went "ballistic" and was "not under control" during the practice interview.
"Imagine your lawyer telling you 'you're disabled' and you can't testify because you can't tell the truth. You just make things up," Woodward said.
In the latest revelation from Bob Woodward's new book, President Donald Trump suggested increasing the personal income tax rate by 4 percentage points.
Shifts in personal attributes were being driven by the leanings of independents, the poll suggested.
"The response was jarring, so different," Woodward wrote of Trump's reply.
A new excerpt from the book obtained Wednesday by The Atlantic showed that numerous questions posed to the president by Dowd pertained to Flynn's conversations with a former Russian ambassador, Sergey Kislyak.
The president has already lashed out at claims made in the book.
The TV host also took a dig at apparent comments made by Gen. John Kelly.
Journalist Bob Woodward's new book alleges that the president's chief of staff made disparaging remarks about his boss.
New book by investigative journalist Bob Woodward, titled "Fear: Trump in the White House," is drawn "from hundreds of hours of interviews with first-hand sources, meeting notes, personal diaries, files and documents."
"That's the kind of disloyalty that leads to you leaving, not staying and undermining the president," Rudy Giuliani told CNBC.
"She has direct access, but she didn't come to me. And you know what? That's okay,"
Bob Woodward's "Fear: Trump in the White House" will be released on September 11.
The 1974 book tells the story of the Watergate scandal, and some readers are finding it newly relevant.