The comedian pays rent for his London home to a firm registered in the British Virgin Islands, often referred to as a tax haven, according to the Sun.
Brand, who has previously called for a revolution and appeared at anti-capitalist demonstrations, responded to allegations in a story on the front page of the paper by saying on Twitter that he intended to sue.
In a post directed at the accounts of the Sun and its owner Rupert Murdoch, he wrote: “Hey... I’m gonna sue you and give the money to #NewEraEstate and JFT96.”
Earlier this week Brand joined hundreds of residents and supporters of the New Era estate in Hoxton, east London, in a protest over fears that a takeover by a US investment firm could lead to a massive hike in rents.
JFT96 stands for justice for the 96 in reference to the number of football supporters who died in the Hillsborough disaster.
Earlier this week Brand, 39, lost his cool with a journalist in Downing Street when he was asked how much he pays to rent his east London home.
The celebrity activist became agitated when Channel 4 News reporter Paraic O’Brien challenged him during a protest over the cost of housing.
Brand pointed his finger in the journalist’s face and called him “a snide”.
O’Brien suggested that the housing problem was being exacerbated by the super-rich buying property in the capital.
Brand later discussed the interview on his YouTube news channel, likening it to a “quarrel at a jumble sale”.
The comic and actor said: “I shouldn’t be allowed on television. I’m so easily wound up. What does it matter to me, what have I got to lose, just from this one bloke?
“But I’m a volatile person.”
He went on: “When you talk to a journalist I sort of think it’s a combination of boring and really annoying, and my personality type is not well suited to that kind of environment.”
During the interview, Brand told the reporter: “I’m not interested in talking to you about my rent, mate. I’m here to support a very important campaign.”
When asked about the value of his home, he went on: “It’s rented. We don’t know the value, you would have to talk to my landlord.
“Blessedly, I can afford my rent and I’m prepared to stand up for people that can’t.”
Cutting the interview short, he added: “Snides like you, mate, undermine (the campaign). You’re a snide. All right, let’s do one.”
O’Brien wrote on Twitter: “Is it my job to test tension between private circumstances and publicly held views of celebrities? Yes.”