Bannon emerged from relative obscurity when Trump picked him as campaign chief in August 2016, just three months out from the presidential election that he was then widely expected to loose against Democrat Hillary Clinton.
Besides Bannon, Schiff said those witnesses would include Trump's daughter Ivanka.
In the book, Bannon is quoted as saying a pre-election meeting involving Trump's eldest son Donald Jr. and a Kremlin-linked Russian lawyer was "treasonous".
Former Trump campaign CEO and scorned ex-White House adviser Steve Bannon is expected to be interviewed by the House Intelligence Committee as part of its Russian Federation probe next Tuesday, Reuters reported Thursday. But the Mercer family, the megadonors behind Trump who had also backed Bannon financially, has distanced itself from Bannon, and he had to step down from his post as executive chairman of Breitbart News Network.
Bannon is scheduled to testify in closed session on Tuesday. But while the now former head of right-wing website Breitbart News had no official role in the campaign at the time, he and Trump reportedly knew, liked and talked to each other even before latter's candidacy.
Olympic detente eases North Korean tensions
But Hook said the idea was one of many being explored, and that the allies invited to Vancouver would be consulted. The reason? Both Greece and Colombia sent military forces to fight against the North Koreans.
Under strong criticism from Trump and former White House allies, Bannon backtracked from the comments this week, calling his support for the president "unwavering" and declaring: "I remain ready to stand in the breech for this president's efforts to make America great again".
Corey Lewandowski, Trump's former campaign manager, said Bannon had clearly crossed a line. Politico reported earlier on Thursday that Bannon had hired a lawyer to deal with the probe by the House Intelligence Committee.
Since Robert Mueller was appointed in May to lead the Russia-Trump investigation, four members of Trump's inner circle have been indicted - and two have already pleaded guilty and plan to cooperate with the special counsel's team.
New York Times columnist Michelle Goldberg drew attention to Bannon's comment in on Friday afternoon, shortly after the publication of the Journal report.