"The helicopter was found in the northern Athens suburb of Kapandriti, but there was no trace of the fugitives," an official told the Reuters news agency.
Both men escaped from the same prison three years ago when a hijacked helicopter landed in the jail's central courtyard.
Guards failed to avert the escape after thinking the aircraft's arrival was part of a visit by prison officials.
Paleokostas, 44, was serving a 25-year sentence for kidnapping and bank robbery and awaiting trial at the time of the escape.
He was re-captured in August in Thessaloniki, northern Greece, when police traced the ransom money.
Security is being tightened around Palaiokostas' brother Nikos, who masterminded the escape and is currently in prison.
Korydallos holds some of the country's most notorious criminals, including the leaders of the organisation, November 17, who were found guilty of murdering politicians, businessmen and foreign diplomats.