The target list includes Tennessee Sen. Bob Corker, Mississippi Sen. Roger Wicker, Alabama Sen. Luther Strange, Nevada Sen. Dean Heller and Arizona Sen. Jeff Flake, the source said.
Flake, a strong critic of Trump, has not backed down from the President in the wake of Trump's public attacks against him.
The news comes as Bannon claimed "the Republican establishment is trying to nullify the 2016 election" in an interview that aired on "60 Minutes" Sunday night
When asked by CBS' Charlie Rose who in the GOP establishment opposed Trump's agenda, Bannon named Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan specifically.
"They do not want Donald Trump's populist, economic nationalist agenda to be implemented," Bannon said. "It's very obvious."
Asked about attacking the very people Trump needs to enact his policy proposals, Bannon said GOP leaders won't provide such help "unless they're put on notice."
"They're going to be held accountable if they do not support the President of the United States," he said. "Right now there's no accountability. ... They do not support the President's program. It's an open secret on Capitol Hill. Everybody in this city knows it."
Bannon has held private meetings with possible challengers whom he plans to support in the primaries, Politico reported. He has begun working with conservative mega-donor Robert Mercer and has installed an ally in an outside group that is expected to target GOP lawmakers and push Trump's agenda, the article said.
Bannon was ousted in mid-August amid a reshuffling of power within the White House, just a few weeks after retired Marine Corps Gen. John Kelly took over as chief of staff with a goal of instilling order in a chaotic operation beset by internal divisions, staff infighting and a storm of controversies.
Bannon has since returned to his role as executive chairman at the conservative online publication Breitbart News, a job he held before joining Trump's campaign.
Bannon is currently in China, where he will deliver a keynote address Tuesday on the subject of "American economic nationalism, the populist revolt and Asia" at an event organized by Hong Kong brokerage firm CLSA.