President Trump entertained the idea of his son-in-law and senior adviser Jared Kushner possibly becoming the future secretary of state, according to an excerpt in Michael Wolff's new book, "Fire and Fury: Inside Trump's White House."

Wolff writes that in an early meeting with Mr. Trump after becoming chief of staff, John Kelly had Mr. Trump's daughter Ivanka Trump and Kushner "on his agenda," with the hope of eventually discussing how to encourage their departure from the White House. But Kelly discovered, according to Wolff's book, that the president was pleased with their performance, and was open to even bigger hopes for Kushner.

"In an early meeting with the president, General Kelly had Jared and Ivanka on his agenda — how the president saw their role; what he thought was working and not working about it; how he envisioned it going forward. It was all intended to be a politic way of opening a discussion about getting them out," Wolff's book says. "But the president was, Kelly soon learned, delighted with all aspects of their performance in the West Wing. Maybe at some point Jared would become secretary of state — that was the only change the president seemed to foresee. The most Kelly could do was to get the president to acknowledge that the couple should be part of a greater organizational discipline in the West Wing and should not so readily jump in the line."

Wolff does not describe how he came to know that particular discussion, although he says he conducted more than 200 interviews for the book and Axios' Mike Allen claims Wolff possesses dozens of hours of recordings of those conversations.

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But the roles of Ivanka Trump and Kushner in the White House has long been a point of tension in the White House. According to Wolff, conservative pundit Ann Coulter told Mr. Trump when he was president-elect that he could not simply hire his children.

"Nobody is apparently telling you this," Coulter told the president-elect, according to Wolff. "But you can't. You just can't hire your children."

The Trump Organization has long been a family affair for Mr. Trump, who handed over the day-to-day running of his companies to his sons, Donald Trump Jr. and Eric Trump, upon assuming the presidency.

The relationship between Mr. Trump and Secretary of State Rex Tillerson has also been under some strain. In November, Mr. Trump said "we'll see" if Tillerson lasts his full first term. Tillerson has insisted he isn't leaving.

CBS News' Mosheh Oinounou contributed to this report.