Bellamy is expected to leave City this summer as he has been told he is not part of manager Roberto Mancini’s plans this season.
Bruce said: “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.
“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.
“I’d think every manager’s looking at City. Steed leaving frees up a wage for us.”
Bellamy has also been linked with a move to Scottish side Celtic.