The book, entitled Rage, is Mr Woodward’s second offering on the Trump presidency. Among other insights into the current administration, it promises to reveal details of 25 letters between the two leaders that have never been made public, an Amazon listing published on Wednesday said.
In one of the letters, Mr Kim described the bond between himself and Mr Trump as something out of a “fantasy film”, according to the publisher.
Rage is set to hit the shelves on 15 September, less than two months before election day.
Simon & Schuster said the book follows “Trump’s moves as he faces a global pandemic, economic disaster and racial unrest”.
It says Woodward, who rose to prominence for his reporting on the Watergate scandal, conducted a series of exclusive interviews with the president.
Woodward’s first book about the Trump presidency, Fear, was published in 2018 and reached No 1 on the New York Times’s bestseller list for nonfiction.
Simon & Schuster was the publisher of two books this year that were harshly critical of Trump: The Room Where It Happened by former national security adviser John Bolton, and Too Much and Never Enough, by Mr Trump’s niece Mary Trump.
Mary Trump has been a thorn in her uncle’s side since the release of the book and has continued to attack his presidency.
In an appearance on The Dean Obeidallah Show on SiriusXM, the president’s niece said that he was liable for American deaths caused by his actions.
“If you have it in your power to save somebody’s life but stand by and do nothing, isn’t that negligent homicide or something like that?” she said in Tuesday’s interview.
“If you are actively withholding personal protective equipment from a state because a governor isn’t nice enough to you and people end up dying, how is that not a crime?”
Additional reporting by agencies