City boss Roberto Mancini has made it clear the 32-year-old Wales international, who spent last term on loan at hometown club Cardiff, is not part of his plans this season.
Bruce has already added nine new faces to his squad this summer, but remains on the lookout following the departure of Steed Malbranque to St 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.”
Hibernian head coach Neil Lennon claimed Craig Levein's comments had come back to haunt him after his side's 2-0 victory over Hearts at Easter Road.
Rangers have been handed a boost ahead of the Old Firm derby at Ibrox on Sunday after Alfredo Morelos signed a new deal that keeps him at the club until 2021.