BBC Sport Wales understands that preliminary negotiations have taken place between the two camps.
Cleverly wants hold the fight in his native Wales but will travel to Las Vegas where Shumenov now lives.
“Beibut Shumenov, the WBA world champion, he’s next in my sights,” unbeaten 24-year-old Cleverly said.
“So whether that’s going to be in Wales or in Las Vegas, where he’s based, we’re yet to find out but wherever the fight takes place I’m really looking forward to that one.”
Shumenov has defended his WBA world crown on three occasions and the 28-year-old from Kazakhstan wants to unify the division, as does Cleverly.
IBF belt holder Tavoris Cloud is another rival challenger in the 175lb division.
“I want to fight the best to be considered the best 175-pounder in the world,” Shumenov said previously.
“All of these guys talking about unifying. Well, if they really want to make it happen all they have to do is contact us.
“I told [IBO champion Jean] Pascal that I’m from Kazakhstan, he lives in Canada; so, we should fight in the capital of boxing, Las Vegas. Same goes for Cleverly, who is from the United Kingdom.
“I’m getting ready and looking forward to a fresh New Year. Hopefully, one of the other light-heavyweight world champions will put his title belt on the line against mine in a unification fight in 2012.”
Cleverly has not ruled out a rematch against Tony Bellew, after defeating the Liverpudlian by points in October.
But whoever he ends up facing, Cleverly says he is yearning to fight in front of a home Welsh crowd for the first time since defeating Joey Vegas in November 2007.
“Preferably I’d love a homecoming now in Wales, it has been a long time,” Cleverly said.
“Most of my fights have been all over the country but a nice homecoming in Wales, that would be another dream of mine – to come to Wales as world champion, defending my title.
“So that would be my number-one venue, otherwise if we’ve got to travel to Las Vegas then so be it. We’ll go out there and do the business.”
Cleverly’s promoter Frank Warren was considering a possible fight against WBC champion Bernard Hopkins but the 46-year-old could be set for a rematch with Chad Dawson following their controversial in October.
There has also been talk of a possible all-Welsh clash with Enzo Maccarinelli, after the former WBO cruiserweight champion made a successful debut at 175 lbs after deciding to step down a division.