Bellamy is currently preparing to represent Team GB at the Olympic Games, but speculation has continued to mount over where he will be plying his trade for the upcoming season.
Liverpool boss Brendan Rodgers has expressed a desire to keep the Welshman at Anfield, while Cardiff are thought to be interested in re-signing their former player.
Bhatia has now confirmed the Hoops are also keen, telling Sky Sports News: "Mark (Hughes) likes to have a long list of players so we'll see what happens.
"We've been a fan of Craig Bellamy for the last few years.
"His is definitely a name that has been mentioned but he's not the only name that we have discussed for that position so we have a few options.
"Mark has loads of names on his list and many of the players we want are wanted by other clubs."
He added: "Whoever Mark settles on, we will do our best to support him."