Vaughters also said in his affidavit that Armstrong blamed the spread of his cancer on the fact that the International Cycling Union (UCI), the sport's governing body, didn't detect high levels of Human Chorionic Gonadotropin in his body when it tested the cyclist, NYdailynews.com reports.
The drug, known as hCG, is taken by males who are steroid users to boost their natural testosterone levels and prevent testicular atrophy.
Vaughters revealed he had a conversation with Armstrong in which he told him that the UCI should have detected a high level of hCG in his doping controls when he had cancer but failed to do so.
Vaughters further added that Armstrong then told him that if he ever has a doping problem then he has this card to play.
Last week, Armstrong admitted to doping during his two-part interview with Oprah Winfrey, and said the PEDs were behind his seven Tour de France victories, titles which have since been stripped from him by the United States Anti-Doping Agency.
Armstrong told Winfrey that he did not think PEDs were responsible for his cancer, which he was diagnosed with and battled before his Tour victories.