It is believed to be the first time Mr Mueller has used such a move against a member of Trump’s inner circle, according to a source from the New York Times.
A spokesman for the special counsel declined to comment.
In the controversial Trump expose “Fire and Fury” Mr Bannon is believed to have described a meeting in Trump Tower between campaign officials and a Russian lawyer as “treasonous”.
The meeting featured the President’s son Donald Trump Jr, his son in low Jared Kushner, then-campaign manager Paul Manafort and Kremlin linked lawyer Natalia Veselnitskaya.
It was set up after a trusted middleman claimed Russia wanted to hand over information that would “incriminate” Mr Trump’s then-rival Hillary Clinton.
In the book, Mr Bannon added: “They’re going to crack Don Junior like an egg” – in comments that caused a public spat between the former Special advisor and the President he served.
Bannon later said his “treasonous” comment was directed at a former Trump campaign manager, Paul Manafort, who also attended the meeting at Trump Tower.
The author of the book, Michael Wolff, disputed Bannon’s account.
Mr Bannon appeared at a separate meeting held by congress on the Russia scandal on Tuesday.
The legal summons was served to Mr Bannon last week, however some believe it may be an attempt to convince the alt-right figurehead into meeting the special counsel in his Washington office to avoid a public spectacle.
Last week Mr Bannon stepped down from his position as Executive Chairman of Breitbart news after a feud with the President over the controversial expose.
The right-wing news organisation confirmed the move on its website after the former White House chief strategist was quoted in the tell-all book criticising President Donald Trump.
Mr Bannon served as a chief adviser to Donald Trump during his campaign, helping him to craft his ‘America first’ policy style.
However Trump is believed to have taken issues with claims the alt-right figurehead was pulling the strings after he was dubbed ‘President Bannon’ by some in the US media.
Several months into Trump’s tenure as President, the controversial political figure was fired from the White House.
In a statement Breitbart Chief Executive Larry Solov said: “Steve is a valued part of our legacy, and we will always be grateful for his contributions, and what he has helped us to accomplish.”
Wolff’s book, “Fire and Fury: Inside the Trump White House,” characterised Trump as mentally unstable, inept and unprepared for the presidency.
Bannon joined Breitbart in 2012 and helped raise the profile of the news site, which he once called the platform for the so-called alt-right, a loose confederation of neo-Nazis, white supremacists and anti-Semites.
“I’m proud of what the Breitbart team has accomplished in so short a period of time in building out a world-class news platform,” Bannon said in a statement cited by Breitbart News.