Milan and Inter in talks over Silvestre move
The 28-year-old made 20 appearances during his first full season at Inter, following a move from Palermo, and Galliani has confirmed that discussions are ongoing.
With Daniele Bonera having fractured his kneecap on Saturday in the International Champions Cup win over Valencia, Galliani has spoken with Inter officials in an attempt to agree a deal for Silvestre.
"We're in talks with Inter for Silvestre. Now I will meet with the Inter directors to find an agreement," said Galliani.
"We still haven't agreed upon what kind of deal it will be for Silvestre."
Brazilian forward Robinho was another Milan player forced off during the clash at the Estadio Mestalla.
Milan hope to have the 29-year-old back in time for the UEFA Champions League play-offs, which get under way on August 20 and 21.
Galliani also confirmed M’Baye Niang would not leave San Siro before the club make their bow in this year's competition.
"We're counting on having Robinho ready for the Champions League play-offs," he continued.
"If Niang leaves Milan then it won't be before the Champions League play-offs."