Milan have sent an offer to Manchester City for the wantaway forward, although the English Premier League leaders are believed to have rejected that.
Galliani says Milan are prepared to be patient in their quest to land the 27-year-old but insists that it is the unavailability of Antonio Cassano that has necessitated a move for Tevez and not a desire to shift one of the rossoneri's current players.
"If Tevez or another striker should arrive it's due to Cassano's problem but (Zlatan) Ibrahimovic, Robinho and Pato are not for sale," said Galliani.
"I know that this morning there was a meeting between (Tevez's agent) Kia (Joorabchian) and City but I don't yet know what happened.
"Unless he signs for another club, we will wait until the last hour, the last minute and the last second of 7pm on January 31 (when the transfer window closes)."
Cassano had to undergo a heart operation last month after being taken ill following a game against Roma.
He was diagnosed with a hole in his heart that needed to be fixed and he has been ruled out until at least April, perhaps longer.
French club Paris St Germain are also believed to be interested in landing Tevez although the press in Italy claim the Argentine only wants to come to this country.
Milan have offered to take the striker on loan until the end of the season with an option to buy him for 23 million euros in the summer.
But Manchester City have said they will not consider a loan deal and will not sell him unless their asking price—believed to be considerably higher than Milan's offer—is met.
If Milan cannot land Tevez they will turn their attentions to Catania's Argentine forward Maxi Lopez and Galliani doesn't envisage any problems with that deal.
"Catania know what the situation is, we have an excellent relationship with (them), they know we're waiting for certain events," added Galliani.
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