Bolton are keen to bring in the Zimbabwe international in January to add to their attacking options.
Benjani is expected to be interested in a move away from City after falling down the pecking order a tthe club, due to the arrivals of Emmanuel Adebayor, Carlos Tevez and Roque Santa Cruz.
Sky Sports says City could be ready to accept a £1.5million bid for Benjani.
Wigan and West Ham are also reportedly monitoring the striker’s situation at Eastlands.