By Karen Freifeld and Patricia Zengerle

WASHINGTON (Reuters) - Former White House strategist Steve Bannon has reached agreement with U.S. Special Counsel Robert Mueller to be interviewed by Mueller's investigators rather than appearing before a grand jury, a source familiar with the matter said on Wednesday.

Bannon, who was a close adviser during President Donald Trump's 2016 election campaign and in his first months in office, had been subpoenaed to testify before a grand jury in Mueller's probe of links between Russia and Trump's campaign.

But the source, who spoke on condition of anonymity, said Mueller offered Bannon the option of being interviewed instead and Bannon accepted. It was unclear when the interview would take place.

An interview with prosecutors would allow Bannon to have an attorney present during his appearance, as lawyers are not permitted in grand jury rooms.

A spokesman for Mueller declined to comment on the agreement, first reported by CNN. A lawyer who represented Bannon in an appearance before the House of Representatives Intelligence Committee on Tuesday could not be immediately reached.

Bannon was fired from his White House job in August as the president sought to bring more order to his staff operations.

Earlier this month, Trump attacked Bannon for comments he made to Michael Wolff, the author of a book highly critical of the president and his family. They included scathing remarks about Donald Trump Jr., the president's eldest son, for meeting during the campaign with a Russian lawyer who was said to have damaging information on Democratic candidate Hillary Clinton.

Mueller is investigating any potential collusion by Trump's campaign with Moscow in alleged Russian meddling in the 2016 election. Russia denies such interference and Trump has denied any collusion.

According to a person familiar with the arrangement, the attorney who represented Bannon for Tuesday's House appearance, William Burck, is not representing him in connection with Mueller's investigation. The person said they did not believe Bannon had hired counsel for that yet.

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A House committee aide declined comment on media reports that Bannon could return to testify again as soon as Thursday.

Two other Trump associates, White House Deputy Chief of Staff Rick Dearborn and former campaign manager Corey Lewandowski, appeared before the House panel behind closed doors on Wednesday, congressional sources said.

Representative Adam Schiff, the panel's ranking Democrat, told reporters that Lewandowski refused to disclose information to the committee about events after he left Trump's campaign. He also declined to say whether he had spoken to Trump about his testimony, Schiff said.

Schiff said Lewandowski was unprepared and would return to the panel another time.

An attorney for Lewandowski did not immediately return an email seeking comment.

The House Intelligence Committee is conducting one of three congressional investigations of the Russia issue, separate from Mueller's probe.

(Additional reporting by Susan Heavey and Jonathan Landay; Writing by Tim Ahmann and Warren Strobel; Editing by Frances Kerry and Cynthia Osterman)