The WBO light-heavyweight champion has been sparring at the trainer's gym in California ahead of his title defence against Shawn Hawk on Saturday evening and Cleverly has revealed that he will consider asking the 52-year-old to coach him in the future.
"Freddie has said some very kind words and is impressed with my sparring," he said.
"That is good because Freddie is a renowned top-class trainer and has worked with many of the top fighters so that is a compliment.
"And it means a lot to me for someone like that to say he'd train me. It's maybe an option."
Roach recently parted ways with Amir Khan.