The Daily Star reports that the Italian giants have made the Argentine one fo their main summer targets.
Tevez has just over 12 months left on his current £200,000-a-week contract at City, who are prepared to sell the striker.
AC Milan have offered Tevez a three-year contract worth a reported £5m a season.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.