The Milan CEO suggested earlier this week the San Siro side could rival the Turin giants for the 29-year-old's signature, allegedly angering the Juventus chiefs with his comments.
However, Galliani has made it clear Milan do not feel any obligation towards Juve to stay away from Tevez.
"I have not heard anything from Juventus and I don't know why they would have any reason to be upset," Galliani told reporters. "I have not talked to Tevez, but I might do so in the future. Either way, we are not doing anything illegal by talking to the player.
"We have not opened talks with City at the moment, but they know that we have been their best customers in recent years. We took Robinho, Nigel de Jong and Mario Balotelli from them."
Tevez has a contract with Manchester City until 2014, but he is keen to leave the club this summer.