Less than three months ago, Nikki Haley, President Trump’s first U.S. ambassador to the United Nations, shut down speculation that she was seeking to replace Vice President Mike Pence on the Republican 2020 ticket.

“Enough of the false rumors,” Haley tweeted on Aug. 21. “Vice President Pence has been a dear friend of mine for years. He has been a loyal and trustworthy VP to the President. He has my complete support.”

But the speculation has resumed during Haley’s promotional tour for her new book, which some observers believe is doubling as an audition for the role of Trump’s running mate.

The cover of Haley's new book. (Image: Amazon.com) More

Haley’s book, “With All Due Respect: Defending America With Grit and Grace,” which was released Tuesday, is respectful toward Trump and dismissive of some of his Cabinet members, including former White House chief of staff John Kelly and ex-Secretary of State Rex Tillerson, who she says tried to recruit her to “save the country” by undermining Trump.

“Kelly and Tillerson confided in me that when they resisted the president, they weren’t being insubordinate, they were trying to save the country,” Haley writes. “We are doing the best we can do to save the country, they said. We need you to work with us and help us do it.”

Both Kelly and Tillerson denied they were trying to undermine Trump. (Kelly told the Washington Post that if providing the president “with the best and most open, legal and ethical staffing advice ... is ‘working against Trump,’ then guilty as charged.”)

Haley says she refused to go along with the idea.

“Go tell the president what your differences are, and quit if you don’t like what he’s doing,” Haley told CBS News anchor Norah O’Donnell. “But to undermine a president is really a very dangerous thing.”

In an interview with NBC’s “Today” show, the former South Carolina governor said she told Trump about Kelly and Tillerson’s backdoor approach.

In the same interview, she defended Trump’s requests for Ukraine to investigate his political rivals in exchange for military aid — the basis of the House Democrats’ ongoing impeachment inquiry.

While she refused to say whether she agreed with Trump that his July 25 phone call with Ukrainian President Volodymyr Zelensky was “perfect,” Haley echoed a White House talking point that there was no pressure put on Zelensky.

“I think it’s never a good practice for us to ask a foreign country to investigate an American,” she said. “Having said that, there’s no insistence on that call. There are no demands on that call. It is a conversation between two presidents that’s casual in nature.”

Haley was also asked if she believes Trump — who the Washington Post estimates has made more than 13,000 false or misleading claims as president — is truthful.

“Yes, in every instance that I dealt with him, he was truthful,” she said.

U.N. Ambassador Nikki Haley with President Trump in the Oval Office in 2018. (Photo: Jonathan Ernst/Reuters) More

For those speculating about Pence’s future, Haley’s overtly pro-Trump PR tour has not gone unnoticed. The president’s change of his official residence from New York to Florida last month also removes the constitutional obstacle to running with Haley, who now lives in New York. The 12th Amendment creates a procedural difficulty for candidates for president and vice president who are residents of the same state.