The Rossoneri official stated that there has been an 'assault' for the highly-rated defender, but insisted that he will hang up the phone on all interested parties
The Brazilian centre-back is believed to be one of the most sought-after players in Europe, with Barcelona, Paris Saint-Germain and Manchester City all linked with the 27-year-old.
City coach Roberto Mancini visited Milan's headquarters on Monday, and it is understood that a big-money offer for Thiago Silva was discussed, but Galliani insisted that the player will not be going anywhere.
"There is an assault on him," Galliani told reporters. "Every big Spanish and English club want him.
"Mancini's visit, however, was just one of courtesy. Thiago Silva will stay at the club, we will resist all temptations, and there are some very strong ones.
"All of Europe want him, but we will resist. There are clubs who have a great economical power, but we will do everything to keep him.
"The same thing applies to Zlatan Ibrahimovic, he will stay at Milan."
Thiago Silva, who joined Milan from Fluminense in 2008 in a €10 million deal, has a Rossoneri contract until 2016.