The 28-year-old Argentine centre-back had been heavy linked with a move to Parma this summer, speculation that grew after he was omitted from Inter's summer training camp.
But club executive Pietro Leonardi has claimed that the interest in Silvestre is now over due to the player's reticence about a move.
"Parma have waited for him many times," Leonardi told Sport Italia.
"But we only sign players with enthusiasm and for this reason we decided not to continue negotiating with the player."
Silvestre is now being linked with a return to his homeland to play for Boca Juniors.