The extension is the third time Bannon's interview has been postponed.
Bannon though is likely to defer to President Donald Trump on the scope of his testimony.
Earlier Monday, Representative Mike Conaway, a Texas Republican who is running the Intelligence Committee's investigation, said that Bannon had been subpoenaed to appear before the committee Tuesday.
Amanda Gonzalez, a spokeswoman for Rep. Trey Gowdy of SC, says the committee extended the deadline on Bannon's subpoena until next Tuesday.
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. "We look forward to having him before the Committee once we can assure that he will be able to thoroughly answer all our questions without concerns regarding the scope of executive privilege".
Mr. Bannon had a very public fall from grace early this year after being quoted extensively in Michael Wolff's tell-all book "Fire and Fury: Inside the Trump White House" and has thus far had a return interview with the House Intelligence committee pushed back three times.
Committee members from both parties have denounced the White House's prohibitions, and stated that they could hold Bannon in contempt of Congress.More news: Bulls reportedly trading Nikola Mirotic to Pelicans
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A follow up hearing on January 18 was postponed after Bannon's lawyers raised concerns about what he could be asked by panel members.
Moscow denies meddling in the presidential election, and Trump denies any collusion between his associates and Moscow.
Trump's staff have tried to utilize the concept of executive privilege to withhold information from the committee.
Things haven't gone Steve Bannon's way since he got on the wrong side of President Trump.
One of the people says Bannon plans to tell Mueller "everything" he knows.
The White House did not immediately respond to a request for comment and neither did an attorney for Bannon. Conaway said. "There are questions that need to be answered".