The Italian side have bid around £21m for the player, who has been absent in his native Argentina since a public spat with Roberto Mancini in November.
Inter Milan have insisted that their bid has not been rejected, but City are understood to want more for Tevez.
"The offer is £25m. Now it's up to them whether they accept it or not," Inter president Massimo Moratti said.
Carlo Ancelotti's Paris Saint-Germain are also said to be interested in the Argentine.