Nikki Haley said the former secretary of state Mike Pompeo’s claim that she plotted to replace Mike Pence as Donald Trump’s vice-president was “lies and gossip to sell a book”.

The former United Nations ambassador spoke to Fox News on Thursday evening, after the Guardian obtained a copy of Pompeo’s forthcoming memoir, Never Give An Inch, and reported his comments about Haley.

Haley resigned from the Trump administration in October 2018. Before that, Pompeo says, she set up a personal meeting with Trump in the Oval Office without checking with him.

Pompeo writes that John Kelly, then Trump’s chief of staff, thought Haley had in fact been accompanied by Ivanka Trump and Jared Kushner as they presented “a possible ‘Haley for vice-president’ option”.

Pompeo also writes unfavourably of Haley’s performance as UN ambassador and criticises her resignation.

Speaking to Fox News, Haley said: “I don’t know why he said it, but that’s exactly why I stayed out of DC as much as possible, to get away from the drama.”

She also pointed out that Pompeo says in his book he does not know if the story is true.

Haley and Pompeo are among possible contenders for the Republican presidential nomination in 2024, a contest in which Trump remains the only confirmed candidate.

But Haley seems set to run.

She told Fox News: “We are still working through things and we’ll figure it out. I’ve never lost a race. I said that then I still say that now. I’m not going to lose now.”

Haley turns 51 on Friday. In a remark seemingly directed at Joe Biden, who is 80, but also Donald Trump, who is 76, she said: “I don’t think you need to be 80 years old to go be a leader in DC. I think we need a young generation to come in, step up and really start fixing things. Can I be that leader? Yes, I think I can be that leader.”

The former South Carolina governor has attracted support from Kushner’s family. She told Fox News Kushner and his wife were her friends, though she expected they would support Ivanka’s father.

She said: “May the best woman win.”

Pence, the senators Ted Cruz and Josh Hawley and even the former national security adviser John Bolton are among other possible candidates for the Republican nomination. But two men, Trump and the Florida governor, Ron DeSantis, dominate polling so far.

On Thursday, Ben Rhodes, a former foreign policy adviser to Barack Obama, wrote: “Pompeo and Haley poised for a real battle to see who can crack 1% in a Republican primary.”

Pompeo’s description of Haley’s supposed meeting with Trump chimed with reports that in 2019 prompted Trump to deny considering replacing Pence as vice-president.

On Thursday, Maggie Haberman, the New York Times reporter and author of the bestselling book Confidence Man: The Making of Donald Trump and the Breaking of America, noted that Kushner and Ivanka Trump “insisted to disbelieving colleagues and Pence allies that they had no role in the Haley/VP rumors”.