Reports in Italy claim the Serie A leaders are targeting Espanyol left-back Didac Vila.
Despite signing Urby Emanuelson from Ajax last week, the Rossoneri need Champions League cover as the Dutchman is not eligible to feature in the European competition.
Galliani said: "Our negotiations are focused on a left-back that doesn't play in the Italian league.
"I cannot reveal his nationality but he should be available to play in the Champions League.
"We need a left-back as an alternative to Luca Antonini considering the injury to Gianluca Zambrotta."
Milan's hopes of signing Italy international Domenico Criscito proved unsuccessful, with Genoa confirming the player will not leave the Luigi Ferraris stadium at least until the summer.
The 22-year-old Didac has made 13 league appearances for Primera Division side Espanyol this season.
