The Rossoneri director has stressed that the Argentine forward is not an option at this point as they already have enough attackers
Juventus now lead the race to sign the forward, having opted to pursue the former Manchester United frontman ahead of more expensive alternatives such as Gonzalo Higuain and Stevan Jovetic.
The Milan director recently hinted at a summer move for the Argentina international, but he has now made it clear that the Rossoneri have no intention to bring in an extra attacker until one of their current forwards leaves the club.
"Tevez is not a transfer target for us. Before we will try to bring in new players, we will have to sell some of our own players first," Galliani told reporters.
"It's not a financial problem, but has to do with the amount of attackers we already have. At the moment, we already have seven players for just three positions.
"Our big transfer coup came in January when we signed Mario Balotelli from City. We will see if anything else happens."
The 29-year-old Tevez has a contract with Manchester City until June 2014, but he is keen to leave the club this summer.