Kelly, however, responded that it would be hard for him to force Jared and Ivanka to give up their positions in the White House without Trump's explicitly telling them he wanted them out.
The Kushners and the White House have already issued denials.
After President Trump's infamous "both sides" flap in Charlottesville in 2017, Gary Cohn sought out advice from Trump's daughter and son-in-law as he mulled resigning over the President's racist comments. In a statement late Monday, Mr. Cohn said: "Ivanka and Jared brought me into the administration".
The book depicts the couple - dubbed "Javanka" by Ward - as both omnipresent and omnipotent, forcing their will upon White House staffers and lashing out at enemies real and perceived when rebuked.
"You've got to be insane", Cohn reportedly scolded Kushner.
The then-secretary of state "told Kushner that his interference had endangered the US", Ward reported in her book, a copy of which was obtained by The Guardian.
Catherine gives rare update on Prince Louis on special day out
Supermodel Kate Moss was pictured heading home with her beloved boyfriend Count Nikolai von Bismarck on Tuesday night. Back in June previous year we first heard that he was crawling when the Duke and Duchess visited Dundee in Scotland.
She was Donald Trump's golden child, the daughter he adored so much, he once explained, that if he weren't her father "perhaps [he'd] be dating her".
After delivering brief remarks with Prime Minister of Ireland Leo Varadkar, Trump answered many questions from the assembled press, with the exception of a tough one from NBC News White House Correspondent Kristen Welker.
According to the book, Kelly told the president at the time that it would be problematic to fire them but later agreed with Trump that they "would make life hard enough to force the pair to offer their resignations".
In response to the book, a representative for Kushner said "It seems [Ward] has written a book of fiction rather than any serious attempt to get the facts".
Meanwhile, Kushner's spokesman tells The Times, "Every point that Ms. Ward mentioned in what she called her "fact checking" stage was entirely false".
He added: "Correcting everything wrong would take too long and be pointless".