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"No, I've never met the guy," Ryan told CNN host Jake Tapper.
Ryan continued: "I don't know Steve Bannon. I have no concerns. I trust Donald's judgement and I think he's going to pick who he thinks will best serve him."
Bannon and Reince Priebus, the chair of the Republican National Committee, were both being considered for the role.
As executive chairman of Breitbart, Bannon directed the website to fiercely attack Ryan. Breitbart has characterized the Wisconsin Republican as a spineless leader who betrayed conservative principles when he assumed his leadership position.
Moreover, emails obtained by The Hill revealed Bannon's end goal was to remove Ryan as speaker.
Nevertheless, Ryan said on Sunday he was "sure" he would be able to "work well with whoever" Trump selects as his chief of staff.
Kellyanne Conway, Trump's campaign manager, said on Saturday the decision on Trump's chief of staff was "imminent."