Ahead of Mayweather's second bout with Marcos Maidana on Saturday night, Roach has questioned the American's fitness, and suggested that Khan is quick enough to cause problems for the unbeaten world champion.
"I'm convinced his legs are shot," Roach told The Guardian. "Look at the first four rounds of the first [Maidana] fight.
"It is his speed that would be the difference. He's just too fast for Mayweather."
Roach, who currently trains Manny Pacquiao, previously worked with Khan.