Serie A champions Milan are short of attacking options, with forward Antonio Cassano sidelined for six months following heart surgery.
The club have been linked to Drogba before, and with the Ivory Coast international struggling to hold down a first-team place at Stamford Bridge, a temporary move to the San Siro could be possible.
“I have been in love with Drogba since he was playing with Marseille,” Galliani told La Gazzetta dello Sport.
“It’s not a given that someone will come in January. If they do it will be on loan because I promised Cassano we will keep his place for him.”
Drogba has made seven appearances for Andre