The former aide to President Donald Trump is to give evidence in the investigation into alleged Russian interference in the 2016 presidential election, according to the publication.
The newspaper’s source reportedly had direct knowledge of the matter.
It is the first time special counsel Robert Mueller has subpoenaed someone from within the US leader’s inner circle.
A spokesman for Mr Mueller has declined to comment.
Mr Bannon had been meeting separately with the US House of Representatives’ Intelligence Committee on Tuesday as part of its own investigation into the Russia allegations.
That meeting took place behind closed doors.
The latest development comes after the former adviser and media executive recently fell out with President Trump over comments he made to Fire And Fury author Michael Wolff.
Wolff says the ex-adviser described a meeting between the President’s son Donald Jr and a group of Russians during the 2016 election campaign as “treasonous” and “unpatriotic”.
The June 2016 meeting involved Trump’s son Donald Jr, son-in-law Jared Kushner, then campaign chairman Paul Manafort and Russian lawyer Natalia Veselnitskaya at Trump Tower in New York.
The meeting came about after Donald Trump Jr was told in an email that the Russian government had compromising information about Democratic presidential candidate Hillary Clinton. Mr Trump Jr is said to have replied: “I love it.”
Wolff wrote that Mr Bannon had told him: “The three senior guys in the campaign thought it was a good idea to meet with a foreign government inside Trump Tower in the conference room on the 25th floor – with no lawyers. They didn’t have any lawyers.
“Even if you thought that this was not treasonous, or unpatriotic, or bad s***, and I happen to think it’s all of that, you should have called the FBI immediately.”
Last week Mr Bannon attempted to backtrack on his comments, saying they were directed at Mr Manafort, who has been indicted on money laundering allegations, which he denies.
Bannon was fired by the White House in August and after the revelations in the Wolff book emerged, the President described him as having “lost his mind” and being “sloppy Steve”.
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A grand jury is a legal entity which can investigate potential criminal behaviour, and determine whether criminal charges should be brought.
Mr Bannon and his representatives are yet to comment.