He was reportedly subpoenaed by former FBI director Robert Mueller, who is leading an inquiry into alleged collusion with Russia during the 2016 election campaign.
Mr Bannon appeared separately on Tuesday before a Congressional panel.
Congress is holding its own inquiry into the allegations.
Mr Bannon was subpoenaed last week, the New York Times reports, quoting an unnamed person with direct knowledge of the matter.
However the summons could be a negotiating tactic by Mr Mueller to persuade Mr Bannon to agree to be questioned by investigators in the less formal setting of the special counsel’s offices in Washington, the paper’s source added.
What is Mr Mueller investigating?
He was appointed by the US justice department in May of last year to oversee an investigation into possible Russian meddling in the 2016 presidential election.
Mr Trump’s campaign and transition teams have been accused of colluding with Russian agents to influence the US election in the Republican candidate’s favour.
US intelligence agencies, including the CIA and NSA, concluded with “high confidence” in 2016 that Russia was behind an effort to thumb the scale of the US election for Mr Trump.
Both the Russian and US presidents have poured scorn on suggestions of collusion, with Mr Trump calling it “the greatest political witch hunt in history”.
Why is Steve Bannon of such interest?
He helped shape Mr Trump’s “America First” election campaign message and served as one of his closest aides before being sacked in August.
But he recently fell out with Mr Trump publicly after reportedly making comments about the president and his family in a newly-published book, Fire and Fury, by Michael Wolff.
Referring to a meeting in June 2016 between Mr Trump’s son and a group of Russians, he was quoted as calling the president’s son, Donald Jr, “treasonous”.