The Rossoneri tried to sign the forward in January, while he was still in dispute with the Premier League outfit, but the deal collapsed over the asking price
The Rossoneri came close to landing the Argentine during the January transfer window, agreeing personal terms with the player only to fail to agree a transfer fee with his English employers.
Galliani speculated at the time that the opportunity to acquire Tevez - who was in dispute with City at the time - was unlikely to arise again, but he has now revealed that he is as determined as ever to make it happen.
"I want Tevez," the 67-year-old Monza native told Corriere dello Sport. "We will do everything to get him."
Rossoneri boss Massimiliano Allegri has already claimed that the club have assured him that his star players, Zlatan Ibrahimovic and Thiago Silva, will not be sold during the summer and that his squad will instead be bolstered by a number of other world-class talents, with Italy international Ricardo Montolivo already on the way from Fiorentina.
Galliani, though, admitted that he will have a tough job in replacing the likes of Alessandro Nesta, Mark van Bommel, Filippo Inzaghi, Gennaro Gattuso and Clarence Seedorf, all of whom are set to make their final appearances for Milan in Sunday's Serie A meeting with Novara at the Giuseppe Meazza.
"I am sad," he told Gazzetta dello Sport. "Those players have kept us on top of Europe for years. Against age, however, there is little to be done.
"But those guys will be missed and will be difficult to replace."
Milan's final game of the season is scheduled to get under way at 15.00CET.