The club has been operating on a shoe-string budget following a period of financial turmoil in which virtually an entire first-team squad was sold off in order to secure a licence and preserve their top-flight status.
AEK are at the bottom of the Greek standings after their worst start to a season.
A group of around 100 staged a sit-in at the premises at Spata on the outskirts of Athens in a peaceful protest with the players training as normal.
"The very idea and club of AEK is dying," a statement from the protesters said. "We have decided to put an end to the rape of our dreams by making an occupation of the club's offices and training centre in Spata.
"We want to put an end to the attack, the humiliation and shaming of our childhood love as a prostitute of Greek football. We now take matters into our own hands by giving an ultimatum to those who are primarily responsible for the misery of AEK."
Club officials have been seeking new investors but, after the recent collapse of a potential deal with London-based investment bank Seymour Pierce, their efforts have been unsuccessful.