The Rossoneri official revealed that there are not enough funds to reinforce the squad after turning down a big-money bid from the Ligue 1 giants for the Brazilian stopper
The French capital club had a €46 million bid for Thiago Silva rejected in June as club president Silvio Berlusconi decided against letting the defender leave.
Milan have already signed Riccardo Montolivo, Bakaye Traore, Francesco Acerbi and Kevin Constant for the new Serie A season, but Galliani revealed that no further purchases will be made.
"We made a huge effort to keep Thiago Silva, it counts as a signing," he told reporters. "We can consider our market closed.
"We will not sign any new midfielder, that area of the squad is complete. Any player could leave, as long as he is not a key member of the team."
Milan offered Thiago Silva a new contract after rejecting PSG's advances, but Galliani rejected the possibility of Kevin-Prince Boateng receiving an improved deal.
"Our players have very high wages, so there will not be an increase in salary for anyone," the Milan official added.