No date has been set for the Mueller interview.
A meeting last week was also postponed.
According to the sources, Bannon's legal team is seeking to determine whether privilege could be invoked to shield their client from questions related to those subjects.
When Bannon appeared before the committee on January 17, he refused to answer some questions, saying he was following White House instructions.
Last month, the panel issued it to force Mr. Bannon to return after he refused to answer their questions about his work on the Trump 2016 campaign and at the White House during a contentious 12-hour session behind closed doors.
Rep. Mike Conaway, the Republican running the committee's Russian Federation probe, told reporters Monday evening he expected Bannon to comply with the subpoena demands of the committee and was unaware of any deal to limit the answers he would provide to the panel.
Also Tuesday, the House intelligence committee gave Bannon another week to negotiate the terms of a closed-door interview.
Bannon left the White House in August.
The House intelligence committee has voted to release a second classified memo about whether the Federal Bureau of Investigation and Justice Department conspired against President Donald Trump.
Bannon Reportedly To Skip Testifying Before House Panel
The panel vote was unanimous to make the classified Democratic document public.
Bannon though is likely to defer to President Donald Trump on the scope of his testimony. The Republican memo criticizes methods the Federal Bureau of Investigation used to obtain a surveillance warrant on a one-time Trump campaign associate. White House officials said they received the memo Monday evening, and press secretary Sarah Huckabee Sanders said the administration "will follow the same process and procedure" it did with the Republican document - meaning Trump has five days to decide whether to allow the memo's publication.
Schiff quickly shot back: "Instead of tweeting false smears, the American people would appreciate it if you turned off the TV and helped solve the funding crisis, protected Dreamers or ... really anything else".
President Donald Trump met with a top Justice Department official Tuesday to review a classified Democratic memo on the Russian Federation investigation, less than a week after he brushed aside objections from the same agency over releasing a Republican account.
Trump last week declassified a document written by the committee's Republican majority that criticized methods the Federal Bureau of Investigation used to obtain a surveillance warrant on a onetime Trump campaign associate.
The Democratic document attempts to counter arguments and evidence presented by committee Republicans.
Trump says on Twitter Monday: "Little Adam Schiff, who is desperate to run for higher office, is one of the biggest liars and leakers in Washington, right up there with Comey, Warner, Brennan and Clapper!" According to the four-page document, the FBI had abused its power in its investigation of the presidential campaign and applied for a wiretap with insufficient context for surveillance. The California Democrat said on ABC Sunday that it was a "political hit job".
And that's both Democrats and Republicans who feel that way. Testifying before the Special Counsel does not obviate Mr. Bannon's obligations under the subpoena issued by the Committee.
The committee rejected that move last week.