The sparring session caught the eye of head trainer Freddie Roach, who believes Cleverly has a very rare talent.
"You want guys like that in your gym," Roach told walesonline.co.uk
"I wouldn't hesitate to take him on, he's definitely talented. We haven't discussed him coming here yet but he's here, and maybe there's a reason why he's here. I think he is at the right stage where a unification fight would be good for him and he has the potential to beat any of the world champions."
"It is a very competitive division right now. There are some good fights out there for him. He's a great boxer but his punching power is not the best in the world. He still has a little bit of an immature style of scoring points and getting out of the way, but sometimes you have to take more chances."
"The passive defence gives you a good defence but you can't slip in a counter punch, that is the best way to knock out guys as you can take advantage of your opponents mistakes."
Cleverly was also delighted with his performance in the sparring session and was extremely pleased with Roach's compliments.
"He said he liked my skill, speed and that I was a really talented fighter," said 'Clev.'
"That is nice because Freddie has worked with the best fighters in the world and that was a good compliment. The climate is brilliant for training and I love Los Angeles."
"It is a great improvement and everybody seems positive in this city. I've got the buzz for this place. I could see in the Wild Card Gym that he lives for that place and his boxing. You can't help but pick up things."
Things got even better for the Welshman this week when Golden Boy promoter Oscar De La Hoya announced that he would love to stage a fight between ring legend Bernard Hopkins and Cleverly in Britain next year.
Overall it seems like Cleverly has had a pretty good time in America so far and has impressed all of the right people. Let's hope that he can top it off with an impressive performance over Shawn Hawk tomorrow night.
By Jack Price @PriceyJ97.