Khedira's contract with Los Blancos expires at the end of this season and the German has been linked with a number of top European clubs.
Milan were said to be firmly in the race, but Galliani has claimed that money would be a problem.
"Khedira is a player who would be great for Milan, but there is one problem. It is that he earns too much," Galliani told tuttomercatoweb.com.
"He would be great for us but we don't know if he'll renew his contract at Real Madrid. Even if he doesn't he would expect big wages."
Khedira is said to favour a move to the Premier League, with Arsenal and Chelsea potential suitors.