The Argentina international’s long-term future at the Citizens is in doubt, with the striker’s current City contract set to expire at the end of the 2013-14 campaign.
The 29-year-old, who has also been heavily linked with a move to Liverpool, has refused to shed light on whether he will pen a new deal with the one-time Premier League champions.
Tévez came close to completing a move to Milan in January before resolving his differences with ex-City manager Mancini, and Galliani hopes the Argentine spurns Juve.
“I would mind a bit if he should go to Juventus, given the friendship we have built with him,” Galliani told Sport Mediaset.
“But the president Berlusconi is right – if Tévez had arrived in Milan, Balotelli would not have come here.
“We also followed Neymar but he was too expensive for us.”
Milan did manage to land another City striker, Mario Balotelli, in January, with the Italy international scoring 12 goals in 13 Serie A appearances.
MORE: The latest football news