Now the 47-year-old multiple-weight world champion, who wants to break his own record and become boxing's oldest world champion, hopes to regain some honour against either Cleverly, WBA title-holder Beibut Shumenov or IBF champion Tavoris Cloud.
Unbeaten American Cloud makes a fifth defence of his title against Karo Murat in Caracas on 24 November.
Cleverly extended his unbeaten record to 25 fights with a fourth successful WBO title defence at Staples Center on Sunday.
The WBO sanctioned the bout against an unranked opponent as long as the Welshman makes a mandatory world title defence against the WBO's number one challenger Robin Krasniqi, probably in Germany, within 90 days of outclassing Hawk.
"There have been talks for a while about the possibility of Bernard Hopkins," said Cleverly.
"Hopkins is a great fighter who is coming towards the end of his career while I'm a young world champion - so that will be a real interesting fight and I'd love a shot at Hopkins."
Cleverly, normally a headline act in the UK, was down the card here in LA as his fifth fight slot was at 5pm - but crucially it was on American television.
Mickey Rourke (left) and Sir Tom Jones (right) celebrate with Nathan Cleverly
He travelled to California hoping to gain some "important American exposure" and has successfully impressed Golden Boy Promotions president Oscar De La Hoya, hall of fame trainer Freddie Roach and American TV moneymen with his fighting style and attitude.
And Golden Boy Promotions chief executive Schaefer insists whether Cleverly fights Hopkins or not, they want him to return to the lucrative United States market on a regular basis.
"Nathan made a great first impression in the United States and first impressions count," Schaefer stated.
"It was an electrifying performance and he won over a lot of American fight fans with his style of throwing a lot of punches and pressing his opponent, that's what American fight fans want to see.
"He has proved he is a name in the light heavyweight division to be reckoned with and I can't wait to have him back her in the very near future.
"Nathan is maybe the most exciting fighter in the division - and the American public now know that Nathan Cleverly is a name in the mix here in the United States.
"It was great seeing
Sir Tom Jones and Mickey Rourke
carrying his belt into the ring and that would have helped his popularity - everybody loves a bit of Hollywood flair.
"Nathan is young, good looking and has a great future but it is important he remains active here in the United States and not make it just a one-off."
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