Cash-strapped AEK, who have been seeking new investors for several months, were embarrassingly forced to have their Super League match against OFI Crete postponed twice this weekend as they were unable to secure tax clearance for the issuing of tickets.
The club faces a UEFA disciplinary hearing on Thursday over its troubled finances.
The desperate situation has prompted reports that the club is seeking to down-grade the team and purchase a new tax number in order to survive.
"As president of the supporters' club I can tell you that nothing of the sort has crossed anyone's mind, while as a member of the executive board I assure you that something like that has not been discussed - not even as a joke," Makis Kasnakidis told Greek radio station NovaSport FM.
He added: "As a fan I would be ashamed if something like that happened. It would not be the team I loved any longer."
AEK's fate in terms of potential sanctions could be more severe than those imposed on Thessaloniki club PAOK last month.
According to Greek media reports, the club must find four million euros before Thursday's hearing in order to avoid heavy penalties.
PAOK narrowly escaped harsh punishment from UEFA over its debts after scrambling to improve finances with player sell-offs just ahead of a disciplinary decision.
UEFA ordered PAOK to pay a 50,000 euro fine and the club was given a June 30 deadline to further improve its finances.
An additional fine of 200,000 euros and a three-year exclusion from European competitions was suspended until the next UEFA review after that deadline.
It is not known when AEK's match with OFI Crete will take place as all next weekend' fixtures have been postponed by the Super League in protest at a new government sports law and the delay by state-run betting compnay OPAP in signing up to sponsorship commitments.
Meanwhile, the two-horse race between leaders Panathinaikos and defending champions Olympiakos Pireaus continued over the weekend with both teams recording victories.
Olympiakos cruised to a 2-0 home win over Panionios on Sunday courtesy of goals either side of half-time from Jean Makoun and Diogo to ensure their remain just two points behind the Greens, who secured a solid 2-0 away win at Ergotelis in Crete 24 hours earlier thanks to second-half goals from Simao and Charis Mavrias.
Panathinaikos are on 52 points with Olympiakos on 52 and fourth-placed AEK on 37.
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