The Rossoneri pulled out of negotiations with City earlier this month to acquire the Argentina forward but have now confirmed they are back in the race to sign the 27-year-old.
"Tevez wants Milan? We also want Tevez," Galliani said on the club's official website, acmilan.com
"We shall see, there are still seven days left until the end of the transfer window."
However, Milan face stiff competition from Paris Saint-Germain and Inter Milan to land Tevez, who has stated his preference to join the Rossoneri.
Galliani insisted that should Milan fail to acquire Tevez, the Rossoneri would sign Fulham target Maxi Lopez from Catania.
"If Tevez does not arrive, then Maxi Lopez will join us," Galliani said. "Either one or the other, certainly not the two of them."
Reports in Italy claimed Lopez travelled to Milan on Monday to complete his transfer to the San Siro outfit.
However, Galliani said: "I think he (Lopez) is already in Milan but we will now see what happens.
"His medical? We must be calm, we need to wait a few more days. Maxi Lopez is a player that interests us a lot and it's likely that he will arrive. The situation is very simple, we have an agreement with Catania and with the player."