According to the Washington Post, Haley writes in "With All Due Respect" that Tillerson and Kelly confided in her that Trump was unsuited for the office of the presidency and they were resisting his directives in the best interests of the country.
"It should've been, 'Go tell the president what your differences are, and quit if you don't like what he's doing.' But to undermine a president is really a very risky thing".
Haley, a former SC governor of Indian descent, left the United Nations job at the end of 2018 on good terms with Trump.
Nikki Haley told CBS on Sunday that she was offended when two top Trump aides attempted to recruit her to undermine the president in order to "save the country".More news: Emilia Clarke hits out at 'bloody annoying' Last Christmas spoilers
"I just couldn't get my arms around the fact that here you have two key people in an administration undermining the president", she said. And it goes against the Constitution, and it goes against what the American people want.
In the interview with CBS, she also criticised House Democrats' moves to impeach the president, saying that impeachment is "like the death penalty for public officials".
In the book, Haley supports numerous Trump foreign policy decisions that others in the administration opposed, including the unilateral withdrawal from the Iran nuclear deal and the Paris climate agreement, as well as the decision to move the US Embassy in Israel from Tel Aviv to Jerusalem.
Haley described her disagreements with Trump over his handling of his meeting with Russian President Vladimir Putin in Helsinki in July 2018, as well as Trump's comments in 2017 where she said he displayed "moral equivalence" in response to a white nationalist march in Charlottesville, Virginia, according to the Post.
In an interview with the Post in her publisher's NY office, Haley dismissed House Democrats' moves to impeach Trump over his pressure on the Ukrainian government to obtain political dirt on an opponent.More news: Russian professor arrested after severed arms found in backpack
Ms Haley, 47, said she had refused the request from Mr Kelly and Mr Tillerson, and called it "dangerous" and "offensive".
Trump's reaction - that both sides had been to blame - was painful, Haley wrote.
"A leader's words matter in these situations. Do I think the president did something that warrants impeachment? No". Trump let him go in December 2018.
"No, it's not appropriate", Haley agreed before defending the Trump. "From the standpoint of: don't bash America over and over again, and not do something to try and fix it".
Haley's book will be released Tuesday.More news: Celtic Gave Us Chances, We Didn't Take Them, Lazio Star Laments