"Fire and Fury: Inside the Trump White House" by Michael Wolff, due out on Tuesday, set off a political firestorm with its portrayal of Trump as not particularly wanting to win the presidency in 2016 and unprepared for the job.
Some of the harshest commentary came from Bannon, the right-wing firebrand who headed the final stage of Trump's campaign and became chief strategist at the White House before being fired in August.
Charles Harder, Trump's personal lawyer, provided a legal notice to Reuters that warned of possible claims including libel against Wolff and publisher Henry Holt & Co and said they would try to block publication of the book.
Harder also told Reuters "legal action is imminent" against Bannon.
Wolff and Holt did not respond to requests for comment.
Trump cut ties with Bannon on Wednesday, saying his former adviser had "lost his mind," in a blistering statement issued after comments attributed to Bannon in the book were made public.
Trump lawyers sent a cease-and-desist letter to Bannon on Wednesday asking him not to disclose any confidential information. They said Bannon had breached an agreement by communicating with Wolff about Trump, his family and the campaign and made "disparaging statements and in some cases outright defamatory statements" about them.
In the book, Bannon was quoted as describing a June 2016 meeting with a group of Russians at Trump Tower in New York as "treasonous" and "unpatriotic." The meeting, held after the Russians promised damaging information on Democratic presidential candidate Hillary Clinton, was attended by Donald Trump Jr., Trump's son-in-law Jared Kushner and Paul Manafort, who was Trump's campaign manager at the time.
Trump's statement also diminished Bannon's role in the election victory and accused him of leaking to the media. Before joining the campaign, Bannon had headed conservative Breitbart News website and he proved to be a divisive figure in the White House. He returned to Breitbart after being fired, although he reportedly continued to talk with Trump.
"CHANGED HIS TUNE"
Bannon's reaction to the book controversy has been muted. In interviews with Breitbart News after the news broke, he called Trump a "great man" and pledged continued support for his agenda.
The president took note. "He called me a great man last night so he obviously changed his tune pretty quick," Trump told reporters on Thursday. "I don't talk to him. That's a misnomer."
Bradley Moss, a Washington lawyer specializing in national security law, said any non-disclosure agreement would not apply to Bannon once he became a government employee. The government has far less power to limit speech by employees than private companies, Moss said.
A lawsuit could hurt Trump because Bannon's lawyers would be entitled to interview White House officials and collect potentially damaging documents from them in his defense, Moss said.
"I assume the cease-and-desist letter is aimed primarily at the public," added Michael Dorf, a professor at Cornell Law School. "The idea that he could block publication is absurd."
On Thursday, the White House said no personal devices, including cellphones, would be allowed in the West Wing beginning next week for security purposes. The moves followed the Bannon split but had been considered for some time.
Bannon helped Trump shape a populist, anti-establishment message and had been the president's link to his hard-line conservative base of support, which is often at odds with the Republican Party establishment.
The story that triggered the Trump-Bannon split was an offshoot of the investigation into whether Trump campaign aides colluded with Russia to sway the election to Trump, allegations Trump and Moscow deny.
