In a new memoir peppered with broadsides at potential rivals in the 2024 Republican presidential primary, Mike Pompeo, the former secretary of state, accuses Nikki Haley of plotting with Jared Kushner and Ivanka Trump to be named vice-president, even while she served as Donald Trump’s ambassador to the United Nations.

Describing his own anger when Haley secured a personal Oval Office meeting with Trump without checking with him, Pompeo writes that Haley in fact “played” Trump’s then chief of staff, John Kelly, and instead of meeting the president alone, was accompanied by Trump’s daughter and her husband, both senior advisers.

“As best Kelly could tell,” Pompeo writes, “they were presenting a possible ‘Haley for vice-president’ option. I can’t confirm this, but [Kelly] was certain he had been played, and he was not happy about it. Clearly, this visit did not reflect a team effort but undermined our work for America.”

The gossipy nugget is contained in Pompeo’s new book, Never Give an Inch: Fighting for the America I Love, which will be published next week. The Guardian obtained a copy.

The Haley story is not the only startling scene in a book which also says Trump had the “nutty idea” that Pompeo could be secretary of state and secretary of defense at the same time.

But the story about Haley is firmly in the vein of Washington reportage and tell-alls that Pompeo claims to disdain. It also adds weight to stories which said Trump did indeed consider dumping his vice-president, Mike Pence, for Haley, a rumor Trump was compelled to deny in 2019.

It will also add to intrigue around reports that Kushner’s family is fundraising for Haley ahead of her 2024 run.

A year out from the primary, Trump is still the only declared candidate for the Republican nomination. But jockeying for position is increasing. Among campaign books from possible contenders, Pompeo follows Pence into print but is a month ahead of Ron DeSantis, the Florida governor who is Trump’s only serious polling rival.

Pompeo is studiedly respectful in his descriptions of Pence, a self-proclaimed fellow devout Christian, and mostly of Trump himself. Unlike Pence in his memoir, So Help Me God, Pompeo avoids overt criticism of his former boss. Pompeo is also more comfortable with the former president’s often vulgar language.

For instance, Pompeo describes Trump calling John Bolton, his third national security adviser, a “scumbag loser”. After being fired, Bolton produced a memoir of his own, The Room Where It Happened. Trump sought to prevent publication but the book was a bestseller, relaying the president’s private conversations and what Pompeo considers highly sensitive material.

Bolton has now floated a White House run of his own, to try to block Trump. Pompeo fires salvos Bolton’s way, at one point comparing him to Edward Snowden, who leaked surveillance secrets to the media in 2013, but saying the National Security Agency contractor “at least had the decency not to lie about his motive”.

Bolton, Pompeo writes, should “be in jail, for spilling classified information”. Pompeo also says he hopes one day to testify at Bolton’s trial on criminal charges.

Regarding Haley, who has also published books as she considers a presidential run, Pompeo disparages both the role of UN ambassador – “a job that is far less important than people think” – and Haley’s performance in it.

“She has described her role as going toe-to-toe with tyrants,” Pompeo writes. “If so, then why would she quit such an important job at such an important time?”

Haley resigned – or, in Pompeo’s words, “flat-out threw in the towel” – in October 2018. By quitting, Pompeo writes, Haley “abandoned” Trump as she had “the great people of South Carolina”, by resigning as governor.

True to his title, Pompeo does not give an inch in his descriptions of his own success, first as CIA director and then atop the state department.

But the former soldier and congressman does spill details of a private conversation in which, he says, the president’s chief of staff said Trump wanted him to add secretary of defense to his portfolio while remaining secretary of state.

According to Pompeo, on 19 July 2020, midway through the tempestuous summer of the coronavirus pandemic and protests for racial justice, Trump’s last chief of staff, Mark Meadows, told him Mark Esper was “not going to make it” at the Pentagon for much longer.

Pompeo says Meadows told him Trump wanted his secretary of state to “dual hat”, meaning to “take on leading the department of defense as an additional duty”.

Pompeo says he told Meadows that was “a nutty idea” as he had “plenty” to do at state and “couldn’t possibly command defense at the same time”.

Nor, Pompeo writes, was that the only time Trump asked him to do two jobs. After Bolton left, he writes, “someone had reminded the president that Henry Kissinger had been both national security adviser and secretary of state” to Richard Nixon and Gerald Ford.

“President Trump pitched the idea to me,” Pompeo writes. “I think he was half-kidding.”

Trump may not feel in a kidding mood when he reads Pompeo’s descriptions of such “nutty ideas” which, the former secretary of state writes, quickly “faded, all for the good”.