The 30-year-old has scored 182 goals in all competitions for Real since his 2009 move from Lyon, but just 10 strikes came in La Liga and Champions League fixtures during the last campaign.
According to AS, quoting a report by esteemed Italian journalist Gianluca Di Marzio, Benzema is believed to be closing in on a move to Milan.
The report claims that intermediary Ludovic Fattizzo and Benzema's representatives held a meeting with Rossoneri coach Gennaro Gattuso and sporting director Massimiliano Mirabelli at Milanello on Monday.
In addition, AC Milan have reportedly promised to match Benzema's €9m (£8m) annual salary at Real, and have offered him a contract until 2022.
Benzema is currently contracted to Real until 2021.