The offer is believed to have been made prior to Lance's recent confessional interview with Oprah Winfrey.
Entertainment Weekly reports that ABC network offered the disgraced former professional cyclist the chance to compete on the forthcoming spring edition of the show.
However sources suggest that Armstrong is one of several "big get" celebrities who are regularly asked to appear on the show.
"Lance has been offered the show each and every year since its inception," a representative for the cyclist told the magazine.
"Although flattered, he has passed on their generous offers."
The sportsman, who claimed seven Tour de France victories, recently admitted to Oprah that he took performance-enhancing drugs during his career.
Lance used EPO (erythropoietin) in the mid 1990s, but claims he was done with drugs by the time of his 1999 comeback.
He was formally stripped of his wins after being accused by anti-doping authorities of using forbidden substances.