The report also claims that the American, who was stripped of his seven Tour de France titles after doping officials produced a huge dossier of evidence against him, was in talks with the United States Anti-Doping Agency.
Tim Herman, Armstrong's lawyer, told the paper: "Lance has to speak for himself on that."
The USADA gave Armstrong a life ban after concluding that he was a part of "the most sophisticated, professionalised and successful doping programme that sport has ever seen" while at the US Postal team.
Armstrong opted not to appeal the ban, which was later ratified by the UCI, world cycling's governing body.
The New York Times said USADA chief Travis Tygart declined to comment on its report.
Last month the Sunday Times launched a £1m lawsuit against Armstrong, who sued the newspaper for libel in 2004 after it raised questions over his success following his recovery from testicular cancer.