The defender is already on the record saying that the Blaugrana approached him about moving to Camp Nou last summer but, the Rossoneri intend to make the Brazilian their new club captain in order to persuade him to remain at San Siro.
However, Galliani claims that the Italian champions are unwilling to listen to offers for the 27-year-old centre-back anyway.
"If Sandro Rosell asks me about Thiago Silva, my answer will be courteous but firm: he is not for sale," the Rossoneri chief is quoted as saying by Tuttosport.
Galliani has the utmost respect for Barca but is still hopeful that Milan can upset the Catalans in the first leg of their eagerly-awaited Champions League quarter-final tie at San Siro on Wednesday.
"I always follow the games of Barcelona as they are a fantastic team," he enthused. "I really like the way they play, they are a great advertisement for football.
"Tonight [Wednesday] they are the favourites, but there are many champions in football and sometimes the favourites lose."
Milan's meeting with Barca at the Giuseppe Meazza gets underway at 20.45 CET.
Between November and February, Goal.com published 10 exclusive extracts from Graham Hunter's highly anticipated new book, 'Barca: The Making of the Greatest Team in the World'. Click here to read all 10 extracts. Don't miss it!