President Massimo Moratti was surprised to read newspaper reports in Italy that the 19-year-old attacker is keen to link up with Arsene Wenger's Gunners in a deal worth some 20 million euros.
Balotelli has had problems in Serie A with the racist behaviour of some opposing fans and his attitude in training has been questioned at times by Jose Mourinho.
It is believed the youngster fancies a switch to London but Moratti has closed the door on a possible exit next month.
Moratti has stated that Balotelli is simply not on the market and he must overcome his problems and prove his worth at the Giuseppe Meazza.
Arsene Wenger is understood to be hunting for a new attacker following the news that Robin van Persie is out for around five months with an injury sustained on international duty with Holland.
Marouane Chamakh remains on his radar but Bordeaux insist they do not want to lose the Moroccan, even though he is out of contract in the summer.
President Jean-Louis Triaud told L'Equipe: "I have no information on this matter.
"In any case, it's out of the question. Marouane is such a decisive player, while we also have important challenges ahead of us, in the league and in the Champions League.
"If we miss out on our objectives, then we will also lose money.
"In any case, we would not do anything against [coach] Laurent Blanc's wishes."
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