The Rossoneri's first choice remains Wolfsburg forward Edin Dzeko but with the Bundesliga club remaining firm that he is not for sale, Milan are starting to look at alternatives.
Galliani indicated on Thursday that they might be interested in Adebayor and it now appears that the Serie A side have stepped up their interest in the Togo international.
"We don't have any agreement with Dzeko," said Galliani. "He is a Wolfsburg player.
"Dzeko has expressed his liking for a move here but at this moment there are no negotiations yet.
"We wrote to Wolfsburg and they responded that he is not for sale. If Wolfsburg change their minds we have agreed they will call Milan. If they do I am ready to immediately leave and go there.
"There's no fee yet, at the moment Dzeko is not for sale. If he becomes for sale then we will start talking sums.
"Adebayor and (Sevilla striker) Luis Fabiano are the alternatives. For Adebayor there has been a telephone call, during which (Arsenal manager Arsene) Wenger was friendly."
Speculation has been rife that midfield duo Andrea Pirlo and Gennaro Gattuso would be joining former coach Carlo Ancelotti at Chelsea.
However, Galliani reiterated that no offers have been made for Pirlo, while Gattuso has offered to take a pay cut to extend his stay at the San Siro.
Galliani said: "There have been no offers for Pirlo and Thursday night with Ancelotti was just a dinner between old friends, seeing as Carletto was in Milan for his daughter's graduation.
"Wednesday night I was at dinner with Gattuso who told us that he was ready to reduce his salary.
"He still has two years left on his contract, so it will move to three years, reducing the salary.
"Gattuso is an example, a true man, extraordinary."
Meanwhile, Davide di Gennaro returns from Genoa after Milan won a blind auction to buy out the other club's half of the players' rights.
The Rossoneri also confirmed that they have beaten off competition from several other Serie A clubs to the signature of 18-year-old Treviso striker Gianmarco Zigoni.
Galliani indicated on Thursday that they might be interested in Adebayor and it now appears that the Serie A side have stepped up their interest in the Togo international.
"We don't have any agreement with Dzeko," said Galliani. "He is a Wolfsburg player.
"Dzeko has expressed his liking for a move here but at this moment there are no negotiations yet.
"We wrote to Wolfsburg and they responded that he is not for sale. If Wolfsburg change their minds we have agreed they will call Milan. If they do I am ready to immediately leave and go there.
"There's no fee yet, at the moment Dzeko is not for sale. If he becomes for sale then we will start talking sums.
"Adebayor and (Sevilla striker) Luis Fabiano are the alternatives. For Adebayor there has been a telephone call, during which (Arsenal manager Arsene) Wenger was friendly."
Speculation has been rife that midfield duo Andrea Pirlo and Gennaro Gattuso would be joining former coach Carlo Ancelotti at Chelsea.
However, Galliani reiterated that no offers have been made for Pirlo, while Gattuso has offered to take a pay cut to extend his stay at the San Siro.
Galliani said: "There have been no offers for Pirlo and Thursday night with Ancelotti was just a dinner between old friends, seeing as Carletto was in Milan for his daughter's graduation.
"Wednesday night I was at dinner with Gattuso who told us that he was ready to reduce his salary.
"He still has two years left on his contract, so it will move to three years, reducing the salary.
"Gattuso is an example, a true man, extraordinary."
Meanwhile, Davide di Gennaro returns from Genoa after Milan won a blind auction to buy out the other club's half of the players' rights.
The Rossoneri also confirmed that they have beaten off competition from several other Serie A clubs to the signature of 18-year-old Treviso striker Gianmarco Zigoni.
