In excerpts of his interview with the CBS network scheduled for Sunday broadcast, USADA CEO Travis Tygart said he had written a letter to Armstrong with the offer.
Armstrong, 41, admitted in an interview with Oprah Winfrey last week that he had cheated his way to a record seven Tour de France titles with systematic use of banned, performance-enhancing drugs. Last year he was stripped of his titles after being labelled a "serial cheat" by the USADA.
Tygart also disputed Armstrong's claims of a clean comeback in 2009.
"His blood tests in 2009, 2010 ... one to a million chance that it was due to something other than doping," Tygart said.