Sources told CBS News that the offer was intended to compensate the U.S. Postal Service for the money it paid to sponsor Armstrong's cycling team from 1999 to 2004.
In addition to the money, CBS said it learned that Armstrong has offered to be a cooperating witness in a federal investigation.
The contract Armstrong had with the postal service banned doping but late last year the U.S. Anti-Doping Agency produced evidence that his team ran "the most sophisticated, professionalized and successful doping program the sport has ever seen."
Armstrong sat down for an interview with Oprah Winfrey that will air on Thursday.
In that interview he offered a limited confession, CBS News has confirmed.
Winfrey told "CBS This Morning" that he "did not come clean in the manner that I expected."
Celebrity Families of 2014 [PHOTOS]