The Rossoneri confirmed the signature of Catania forward Maxi Lopez on Friday evening after they gave up their pursuit of Manchester City outcast Carlos Tevez.
Galliani, who steadfastly maintained that only either Lopez or Tevez would be signed, has now dramatically hinted that another arrival could be announced before the January market closes on Tuesday night.
"[Monday] morning I will be in the office and I will be there up until 1900 [CET] on Jan. 31," he told the Rossoneri's official website after his club's convincing 3-0 win over Cagliari on Sunday night.
"I'm pretty sure that Maxi Lopez is the last of our transfer market signings, but who can know the future?"
The Milan supremo then proceeded to compare forward Zlatan Ibrahimovic to former Milan attacking wizard Marco van Basten after the Swede scored and set up another goal in Milan's comprehensive 3-0 win against Cagliari.
"It's pointless to speak of Ibrahimovic anymore; he's just a fantastic player, everyone can see it," Galliani purred.
"It's amazing, he resembles Van Basten."
Milan are now just trailing Serie A league leaders Juventus by a single point.