Armstrong was stripped of his seven Tour de France titles last year after a lengthy and in-depth investigation by USADA.
In a CBS interview to air on Wednesday night (Thursday AEDT) in the United States, USADA's chief executive Travis Tygart has told the 60 Minutes Sports program he was stunned when he received the offer in 2004.
Tygart added that the agency didn't hesitate to turn it down.
Armstrong's attorney Tim Herman has denied such an offer was made.
"No truth to that story," Herman wrote on Tuesday in an email to AP.
"First Lance heard of it was today. He never made any such contribution or suggestion."
Tygart did not immediately respond to requests from AP for comment.