Despite having less than a year left on his contract, Lacazette remained at the Emirates Stadium during the summer transfer window.
However, the Frenchman has featured for just 31 minutes in the Premier League, making it increasingly likely that he will be allowed to depart the club in 2022.
According to Calciomercato, the Gunners have asked Milan whether they are interested in signing the 30-year-old in January or next summer.
While Arsenal would prefer to recoup a fee for the player in January, any club keen on Lacazette could negotiate a cut-price figure.
The former Lyon frontman last featured for Arsenal on September 22, getting on the scoresheet as his team eased past AFC Wimbledon in the EFL Cup. body check tags ::