Last week the Italian champions signed Argentine forward Maxi Lopez, suggesting their month long pursuit of unsettled Manchester City star Tevez had come to an end.
And Galliani admits that if anything does happen, it will likely be in the summer.
"Maxi represents the present and the important future for Milan, our coach is a big fan of his and so I wish him luck," said Galliani.
"From now until 7pm tomorrow (Tuesday, when the transfer window closes) maybe no-one will join but there could also be a surprise.
"We're not expecting (Tevez) to join, instead we have Maxi Lopez. We'll see what happens in the summer, the transfer window is almost shut.
"Of course, I considered the summer market closed (at the end of August) and then we bought (Antonio) Nocerino at the last minute.
"It's not that sometimes the truth isn't said but that sometimes things develop later, hence right now I would say that nothing will happen."
Although he was always aware of being very much a Tevez consolation prize, Maxi Lopez is still delighted to have joined Milan from Catania.
"I had to wait until the last moment before becoming a Milan player but I was always very confident," he said.
"It was a very strange week but everyone was very clear with me and I always wanted to stay (at Catania if the Milan opportunity fell through).
"Milan are the team of my dreams and I think that someone has to take risks to arrive at certain clubs.
"I knew that sooner or later, ever since I was little, that I would join this club.
"Now I want to do everything to stay here for life, I never want to leave this place."
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