A transfer appeared imminent after the 67-year-old confirmed on Tuesday that he had agreed terms with the Argentine star's agent Kia Joorabchian to push through a transfer and were waiting a response from the Premier League club, but the supremo told Sky Italia that the deal is not yet complete.
"I can confirm the inclusion of Paris Saint-Germain [in the race to sign Tevez], and we are aware [of that]," said Galliani. "I haven't heard from [PSG sporting director] Leonardo as he works for another club and can do what he wants.
"I expect to learn more in the coming days, but there is time to close the deal until the end of the transfer window, even if I would prefer to take him to Italy before."
However, despite the revelation, Galliani remains undeterred in his efforts to bring in the striker, although he admits that the onus is now on forcing City to part with the player on his terms.
"We all know that Manchester City wants to sell the player and we want to loan him," he continued.
"We have to convince them to accept our conditions, but it will not be easy. Tevez? He wants to join Milan."
AC Milan travel to Bologna on Sunday in Serie A action, as they try to keep the heat on league-leaders Juventus.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.