Reports have suggested that Khan has agreed a deal to fight Mayweather in Las Vegas on May 3, and the British boxer's former trainer believes that the 27-year-old could upset the odds to beat the American.
"I've always said Amir has the right style to beat Floyd if he fights correctly and doesn't stay in the pocket too long," Roach told the Ringside Toe 2 Toe Podcast.
"I always thought he could beat him with his speed. I think he's faster than Mayweather and that's what it takes to beat him.
"Floyd might have his hands full on the night."
Khan beat Julio Diaz in his most recent fight last April.