There have been some disagreements over the deal, with Milan initially wanting to take Tevez on loan. However, Manchester City will only entertain an immediate sale for the player.
"We have an agreement with the player, now there's an ongoing negotiation with Manchester City and we expect an answer," Galliani told Sky Sport Italia.
AC Milan coach Massimiliano Allegri was less forthright about the arrival of the former Manchester United striker.
"I heard yesterday from Galliani, but we did not talk about the transfer market," said Allegri.
"I am not thinking about Tevez because for now he's a Manchester City player.
"Do I worry about his period of inactivity [from football]? I'm not talking about players who are not of AC Milan. If and when he comes, I will take a look."
Tevez has not played for City since refusing to warm up against Bayern Munich.