Blues manager Roberto Mancini has hinted the door is open for the Welshman to leave Eastlands, while Bruce is keen on a loan or permanent move for the 32-year-old.
“I haven’t got a wide left player, not a natural one, although we’ve got people who can play there, so we’ll see," he said.
"We’re all looking at Manchester City because they’ve got some great players who can’t even get in the squad. Craig Bellamy is a possibility. He can play wide left and up front so we’ll see.”
Bellamy, who spent last season on loan at Cardiff City, has also been linked with a move to Celtic, with whom he had a loan spell in 2005 while at Newcastle United.