"He showed that he genuinely has the club's best nterests at heart and is free to take up any of the great offers from teams abroad," AEK said in a statement.
AEK are close to bankruptcy with debts of 100 million euros and their directors expect to lose all five of their Greece internationals before next season.
Midfielder Zagorakis, 32, is reportedly attracting interest from teams in France, Spain, Italy and Germany, with local media predicting a swansong at newly promoted Serie A club Bologna.
Eurosport.com XI of Euro 2004
The former Leicester City and PAOK Salonika player is favourite to be given the honour of carrying the Olympic flame on the final leg of its journey into the stadium for the opening ceremony of next month's Athens Olympics.
Santini successor to be named on Friday
Zagorakis named player of Euro 2004