The San Siro chief commented on a number of players who would arrive this summer, including the Genoa duo, but showed the former Arsenal man the exit door
The Frenchman joined the Rossoneri in 2008 following a successful four-year spell at Arsenal, but sat out the majority of last season with a serious knee injury, and that looks to have been a deciding factor in the club's plans.
"His time is up because too much time has passed," Galliani said during an interview in Milan.
"We spoke to his agent and said that we don't expect anything else from the player. By the end of August another midfielder will arrive, which could be [Alberto] Aquilani or someone else.
"We haven't spoken yet to Aquilani. He's a Liverpool player."
Galliani also spoke about the proposed transfers of Genoa duo Francesco Acerbi and Kevin Constant.
"Until we do the medicals we're not saying anything, but [Acerbi] seems healthy," he hinted.
"I think he's a fantastic centre-back with plenty of room for growth which he'll get at Milan. His willingness to come to Milan made the difference.
"[Constant] was snapped up quickly thanks to [Genoa president Enrico] Preziosi, which was very nice. He's a player we wanted last year, and we agreed with the coach [Massimiliano Allegri] when we decided to buy him after learning about [Sulley] Muntari's injury."
The Ghanaian midfielder tore his anterior cruciate ligament and is expected to be out for six months.
"Muntari had a brutal injury. I've never seen such a bad one happen during the summer break," Galliani concluded.