Watch the entire interview below.
Mr Wolff, speaking on NBC's Today Show, denied that claim. "That's the background to the perception and the understanding that will finally end. this presidency".
Later on Wednesday, White House press secretary Sarah Huckabee Sanders fiercely slapped Wolff's book, accusing it is "filled with false and misleading accounts".
Trump, 71, issued the tweets on Saturday from the presidential retreat at Camp David, Maryland, where he was meeting Republican congressional leaders and Cabinet secretaries about their legislative agenda for 2018. I never spoke to him for book.
In the book, Bannon is quoted as saying Ivanka Trump, the president's daughter, and a White House adviser, is as "dumb as a brick".
U.S. President Donald Trump has launched a fresh broadside at his former ally and now-nemesis Steve Bannon, accusing him of crying and begging for his job after he was fired from his position as White House Chief Strategist.
"When you write a book like this, people regret what they said to me", Wolff said in an NPR interview that aired Friday.
"They say he's a moron, idiot".
Mr Bannon is chairman of the so-called alt-right Breitbart News website. He doesn't read. He doesn't listen.
The book infuriated Trump in part by quoting Bannon making derogatory comments about the president's children.
Asked about the possible lawsuits, Stone said, "Yeah, I'm not sure about the efficacy of that".
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