Bannon made the scathing comments in Michael Wolff's book "Fire and Fury: Inside the Trump White House," which is to be published next week.
"They're going to crack Don Junior like an egg on national TV," Bannon reportedly said.
Bannon, who left the White House in August, was also quoted as saying that the investigation by special counsel Robert Mueller into Russian interference in the 2016 election will focus on money laundering.
Bannon joined Trump's election campaign two months after the June 2016 meeting between Russian lawyer Natalia Veselnitskaya and campaign officials.
Donald Trump Jr, Trump's son-in-law Jared Kushner and then campaign chairman Paul Manafort were at the meeting held at Trump Tower in New York.
Donald Trump Jr took the meeting with the Russian lawyer after being promised material that would incriminate Trump's Democratic rival Hillary Clinton.
"The three senior guys in the campaign thought it was a good idea to meet with a foreign government inside Trump Tower in the conference room on the 25th floor -– with no lawyers," Bannon was quoted as saying in the book.
"They didn't have any lawyers.
"Even if you thought that this was not treasonous, or unpatriotic, or bad shit, and I happen to think it's all of that, you should have called the FBI immediately."
The investigation by Mueller, a former FBI director, is looking into whether the Trump campaign colluded with Russia to get him elected -- a charge the president has repeatedly and vehemently denied.
Trump said in an interview with The New York Times last week that he expected the Mueller investigation to be "fair."
Manafort and an associate have been indicted on money laundering charges unrelated to the campaign and Trump's former national security adviser Mike Flynn has pleaded guilty to lying to the FBI.
According to The Guardian, Bannon had particularly harsh comments in the book about Kushner, a wealthy New York property developer who is married to Trump's daughter Ivanka.
"You realize where this is going," Bannon said of the probe by special counsel Mueller.
"This is all about money laundering.
"Their path to fucking Trump goes right through Paul Manafort, Don Jr and Jared Kushner... It's as plain as a hair on your face," he added.
"It goes through Deutsche Bank and all the Kushner shit... The Kushner shit is greasy. They're going to go right through that."
Since leaving the White House in August, Bannon has staked out some positions at odds with the Trump administration.
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![33 passengers and one crew member died on the dive boat, Conception [Brian van der Brug/Los Angeles Times/AP]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "33 passengers and one crew member died on the dive boat, Conception [Brian van der Brug/Los Angeles Times/AP]")
