According to Haley, the two senior officials argued their decisions "were in the best interests of America" because they believed Trump "didn't know what he was doing". It should've been, 'Go tell the president what your differences are, and quit if you don't like what he's doing'.
Some of them went to land book deals, including former White House press secretary Sean Spicer and former communications director Anthony Scaramucci.
"We've solved a lot of problems and we're in the process of solving a lot of problems", the president said, adding that if she chooses to return to his administration, Haley can have her "pick" of jobs.
"The president's words had been hurtful and risky", she wrote, according to the Post.
However, Haley said she supported most of Mr Trump's foreign policy decisions that others in the White House tried to block or slow down, according to the Post.
"Instead of saying that to me, they should've been saying that to the president, not asking me to join them on their sidebar plan", Haley wrote.
In an interview on "CBS Sunday Morning" with anchor Norah O'Donnell, the former governor of SC said she was offended by the two men's comments and that instead of sharing their concerns with her, Tillerson and Kelly should have addressed them directly with the president. Haley writes that she was "shocked" by the request, made during a closed-door meeting, and thought they were only trying to put their own imprint on his policies.
Trump fired Tillerson in March 2018.
There was no immediate comment from Mr Tillerson.
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.
She wrote in her book that she privately expressed concerns to Trump after his meeting with Russian President Vladimir Putin in Helsinki in 2018.
She also wrote that his comments after the deadly white supremacist rally in Charlottesville in 2017, that there were good people on "both sides", had been "hurtful and dangerous". "And the president's words had been hurtful and unsafe", Haley wrote. "Do I think the president did something that warrants impeachment? No".
The daughter of Indian immigrants also didn't agree with Trump's tweets against members of the liberal freshmen "squad" to "go back and help fix the totally broken and crime infested places from which they came".
"No, it's not appropriate", Haley agreed before defending the Trump.