City boss Roberto Mancini has intimated Bellamy's future lies away from the Etihad Stadium this season, as the Italian looks to trim his striking options following the £38 million addition of Sergio Aguero from Atletico Madrid.
Bellamy spent last campaign on loan at Cardiff, scoring 11 Championship goals for the club, and a return to the Welsh club has been mooted. Celtic have also been mentioned as suitors, and now Sunderland have joined the race for his signature after seeing Steed Malbranque leave for Saint-Etienne.
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."