The Manchester Evening News says Interâ€™s new boss Rafa Benitez and owner Massimo Moratti are considering a plan which would see the Brazilian move to the San Siro in a part-exchange deal.
Blues boss Roberto Mancini has already indicated that he would be interested in buying 19-year-old striker Balotelli.
Moratti has indicated that a deal could be done for the teenager, nicknamed Super Mario, if the price was right.
Robinho, who has two years to run on his City contract, has flourished during a six-month stint at Brazilian club Santos, and has indicated that he would like to stay there when that loan deal runs out on August 4.
Santos, however, cannot come close to matching the Brazilianâ€™s City wages of around Â£130,000 a week, leaving a move to Europe the likeliest option.