The Rossoneri have decided to stop negotiations with the defender after talks stalled over him crossing the Milan divide
The Argentine, 28, made just nine Serie A appearances last season, leading to rumours he could trade the Nerazzurri for Rossoneri colours, but Galliani is unhappy with the way talks have progressed.
“Instead of getting closer with today’s talks, we moved further away,” he told Sky Sport Italia.
“Therefore we are looking to other objectives instead. Have we abandoned the Silvestre option? Yes.”
The vice-president was hoping to secure the signature of the defender on a season-long loan after Daniele Bonera suffered a knee injury that will keep him out of action for three months.
Bonera's absence leaves Milan with a dearth of options at the heart of the defence, with Philippe Mexes, Cristian Zapata and Jherson Vergara the only centre-backs on the books after the club sold Mario Yepes and Bartosz Salamon.