The 29-year-old has managed just one goal in 18 appearances for the Rossoneri this season following his summer switch from Serie A champion Juventus.
With Mario Balotelli, Stephan El Shaarawy and Giampaolo Pazzini on the books at San Siro, Galliani has hinted that Matri could be allowed to depart this month, along with one of goalkeepers Gabriel or Marco Amelia.
"Gabriel? Let's see if we part with him or Amelia. Matri? We'll see, we have a lot of strikers. It's possible one might leave," Galliani told the assembled media at new signing Keisuke Honda's unveiling.
Galliani also moved to quash suggestions an inquiry has been made for Chelsea midfielder Michael Essien, though he did suggest Milan will scour the market to find midfield replacements who are eligible for the Champions League.
"It's not absolutely certain a midfielder will come in. Obviously, if one came, he'd need to be available for the Champions League. There are opportunities abroad," he continued. "It's a time when there are thousands of phone calls. Essien? There are no negotiations open for now.
"It's a market where I think many players will move, many want to change team and clubs are willing to sell."