The Italian champions are hoping to land the Argentina international but have yet to reach an agreement with City regarding the transfer fee.
City warned the Rossoneri they would not release Tevez on loan and that they would only accept offers of at least 30million euros.
"We will make a definite decision on Friday," Galliani said to Gazzetta dello Sport.
Should Milan fail in their pursuit of Tevez, the Rossoneri have already agreed terms with Catania to acquire forward Maxi Lopez instead.
Lopez has been in Milan since Monday hoping to complete his permanent transfer to the Rossoneri club.
"Will Maxi Lopez join as well? Who knows," Galliani said.
"I will just confirm that if he doesn't arrive, then we will sign Tevez, but they are two alternative options."
Lopez's agent is nevertheless confident his client will join Milan.
"Opportunities to join a club like Milan don't come often in a career," Lopez's agent Andrea D'Amico said. "They have told us to wait a little bit longer with respect to the 48 hours that had been agreed.
"Milan still has to resolve this situation but we trust Galliani.
"I don't know when but I know Lopez will be a Rossonero player."