The journalist Michael Wolff said Fire and Fury: Inside the Trump White House was based on more than 200 interviews with the President and his staff.
In an excerpt from the book published by New York magazine, the author says Ms Trump and her husband accepted posts as advisers in the West Wing “over the advice of almost everyone they knew” in the hope that his presidency “would catapult them into a heretofore unimagined big time”.
“It was a joint decision by the couple, and, in some sense, a joint job,” Mr Wolff writes. ”Between themselves, the two had made an earnest deal: If sometime in the future the opportunity arose, she’d be the one to run for president.
“The first woman president, Ivanka entertained, would not be Hillary Clinton; it would be Ivanka Trump.”
Former White House strategist Steve Bannon was said to be “horrified” when he heard about the deal.
“They didn’t say that?” he is reported to have said, adding: “Stop. Oh, come on. They didn’t actually say that? Please don’t tell me that. Oh my God.”
Mr Bannon has previously laid bare his disdain for the couple, who he nicknamed “Javanka”, blaming them for being “railhead of all bad decisions” in the White House.
The President’s legal team has sent a letter demanding Mr Bannon "cease and desist" speaking to Mr Wolff after a string of explosive claims emerged in excerpts from Fire and Fury this week.
The threat of legal action comes after the book quoted the former strategist and Breitbart executive chairman as saying a meeting between a Russian lawyer and Donald Trump's eldest son was "treasonous and unpatriotic".
White House aides were caught off guard when excerpts from the book, which portrays Mr Trump as an undisciplined man-child and reluctant President, emerged online ahead of its 9 January publication date.
The excerpts left Mr Trump “furious” and “disgusted,” said White House Press Secretary Sarah Huckabee Sanders, who complained the book contained “outrageous” and “completely false claims against the President, his administration and his family.”
Mr Trump later issued a statement claiming his former strategist had "lost his mind" and had "nothing to do with me or my Presidency".
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