Reports in Italy claim Milan are in the running to sign Siena striker Mattia Destro, who is also a reported target of city rivals Inter.
Liverpool midfielder Alberto Aquilani has also been linked with a move to the Rossoneri outfit having played on loan with the Rossoneri last season.
However, Galliani said to Gazzetta dello Sport: "Milan's transfer market is closed.
"We have nine midfielders and our market is closed."
The Rossoneri have already reinforced their squad with the arrival of defender Francesco Acerbi from Chievo and midfielders Riccardo Montolivo (Fiorentina), Kevin Constant (Genoa) and Bakaye Traore (Nancy).
Moreover, the Rossoneri last month turned down a 46 million euros offer from Paris St Germain for Brazilian defender Thiago Silva.
Milan this week extended Silva's contract for a further season, which will keep the Brazil international at the San Siro until June 2017.
"We must thank (Milan owner) Silvio Berlusconi for keeping Thiago at the club and, hence, resisting the temptation to sell him," Galliani said.
"With regards to those that will depart, only perhaps (Djemal) Mesbah will leave the club."
Mesbah joined Milan in January from Lecce and the Algerian defender is a target of Torino.