A boxing official involved in negotiations but not authorized to discuss details publicly told The Times on Saturday that it's "90 percent" likely that Mayweather (48-0) will fight on Showtime.
Originally, CBS emerged as a player, with Mayweather interested in exploring whether advertising revenue could support a fight of his magnitude.
In May, Mayweather earned in excess of $220 million for beating
Former welterweight world champion Andre Berto is believed to be the favorite to fight Mayweather at MGM Grand in Las Vegas.
Khan (31-3, 19 knockouts), with consecutive wins over former world champions Devon Alexander and Chris Algieri, was believed to be a stronger candidate, but Mayweather has rejected him again after doing so last year before Marcos Maidana.
Khan was removed from consideration, the official said, because he kept publicly criticizing Mayweather after being told to keep his opinions quiet.