The 30-year-old now has less than 12 months left to run on his Gunners contract and is reportedly yet to be offered an extension by the North London club.
Mikel Arteta has backed Lacazette to be "instrumental" for Arsenal this season, but as it stands the ex-Lyon man can negotiate a free transfer with clubs elsewhere from January.
Juventus have been tipped to swoop for Lacazette, but Calciomercato claims that AC Milan also view the Frenchman as an ideal acquisition for their forward line.
The report adds that the Rossoneri are planning for life without Zlatan Ibrahimovic - who turns 40 next month - while Olivier Giroud will celebrate his 35th birthday in just under two weeks' time.
Lacazette boasts 66 goals from 172 games for Arsenal in all competitions but has only played 31 minutes in the Premier League so far this season.