Bellamy, 33, scored nine goals in 33 appearances for the Reds last season after the Wales international re-joined the Merseyside outfit from Manchester City in August 2011.
QPR manager Mark Hughes led the Hoops to safety in their first campaign back in the top flight and the 47-year-old has already strengthened his squad this summer.
Samba Diakité, Robert Green, Andy Johnson, Ryan Nelsen and Park Ji-Sung have all been signed on permanent deals, while Manchester United left-back Fábio da Silva has moved to Loftus Road on a season-long loan deal.
Bellamy worked under Hughes at Blackburn Rovers, when the former Cardiff City striker produced his best ever return with 17 goals in the 2005-06 campaign.
“Craig is definitely a name that has been mentioned, a name we’ve discussed. There are a few options,” said Bhatia.
“We have been a fan of Craig Bellamy for the last few years, ever since he became available – that’s not to say we have not been fans of other players.
“Many names have been tossed about, and who Mark settles on eventually will be his, and we’ll do our best to support him.”
QPR boss Hughes has also been linked with a move for Tottenham Hotspur striker Jermain Defoe, but Bhatia said the England striker is just one of many options that the Hoops are looking at this summer.
“It would be hard to speculate at this point,” added Bhatia. “It’s not the right thing to do. Mark likes to have a long list of players. We’ll see what happens.
“Many of the players we are after potentially have interest from other clubs also.”
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