The 39-year-old, one of AEK and Greece's most popular players, handed himself over to the authorities on Thursday but after brief questioning was released. He is due to give testimony next week to the Athens public prosecutor.
"I gave myself to the authorities of my own accord and gave testimony regarding debts of 35 million euros ($44.94 million)which were restructured during my time as president," Nikolaidis told reporters.
"It is very correct that the state is investigating to find out who has paid and who has not paid. A lot of mud has been thrown but up until the time I left the club everything which was due to be paid was paid on time.
"The legal process is progressing well as far as I am concerned and I hope justice is served because the team is in debt and is dying, and it must be saved."
Current AEK president Andreas Dimitrelos was arrested last week and released on a 40,000-euro bail guarantee as part of the state's investigations into a total of 170 million euros in unpaid taxes.
AEK said the alleged offences occurred before Dimitrelos' tenure at the club, which started last year, and said the tax arrears were being settled under a debt-restructuring procedure initiated by the club under the country's bankruptcy code.
Nikolaidis, who enjoyed a successful playing career with AEK and Greece, took over the presidency in 2004, bringing in investors to help save the club from bankruptcy and certain relegation to the fourth division due to debt problems.
He left under a cloud in 2008 with the club still in financial difficulties after failing to attract a target of 30,000 season ticket holders.
Athens public prosecutor Grigoris Peponis has also issued warrants for the arrest of the club's presidents from 2004 to October 2012, including Giorgos Kintis, Nikos Thanopoulos and Stavros Adamidis.
AEK are 11th in the 16-team Greek Super League after their worst start to a season afflicted by financial struggles.
The club has been operating on a shoe-string budget following a period of financial turmoil in which almost the entire first-team squad was sold last year to secure a Super League licence and preserve the team's top-flight status.
The tax investigation is the latest setback for AEK following the life ban from international football imposed on midfielder Giorgos Katidis by the Greek football federation (EPO) after he made a Nazi salute to fans to celebrate a goal.
The 20-year-old former Greece under-19 captain made the gesture after scoring the winner in a 2-1 league victory over lowly Veria last Saturday.
The club suspended him for the rest of the season after he apologised and asked to be dropped from the first team.