Bellamy, who has a year remaining on his City contract, spent last season on loan at hometown club Cardiff but does not want another loan move, preferring a permanent move away from Eastlands.
He told the Daily Telegraph: "If they pay me the final year of my wages, then I'm sure I can go wherever I want. In that case my first option would be Cardiff."
However, a pay cut does not appeal, as he added: "I have my own academy in Sierra Leone, where I have to take care of 13 children, day in, day out. My wages are more important to them than they are for me.'