Pericles Panagopoulos, founder of Greek ferry operator Superfast Ferries, and his driver were snatched in broad daylight by three armed men in Athens' coastal suburb of Kavouri on Monday, in Greece's third high-profile abduction since June.
The driver, who was left tied to a tree shortly afterwards in the northeast town of Koropi, told police the kidnappers had openly discussed a ransom as the handcuffed captives were driven away inside a van.
"According to testimony, the kidnappers were talking about 30 or 40 million euros in ransom during the abduction," a police official who requested anonymity told Reuters.
A police spokeswoman declined to confirm the information or say if the assailants had contacted the family. State television reported the kidnappers were seeking a 40 million euro ransom.
Police have appealed to the kidnappers to treat the 74-year-old magnate respectfully because of his fragile health.
The kidnapping comes amid the suspected reemergence of left-wing guerrilla group Revolutionary Struggle and was being investigated by anti-terrorist police, but police said it was believed to be the work of a criminal gang seeking a ransom.
Superfast Ferries, which operates mainly routes between Greece and Italy, is a subsidiary of Greece's largest ferry operator Attica Holdings.
In June, the chief executive of aluminium company Alumil and chairman of the Federation of Industries in the northern city of Thessaloniki, George Milonas, was kidnapped before being released two weeks later after a ransom was paid.
Police arrested Greece's most wanted fugitive, Vassilis Palaiokostas, in August for Milonas' kidnapping, after tracing the ransom money.
Last month, a well-known Athens doctor was also kidnapped but has yet to be found. Police are investigating links between that crime and Monday's abduction.
In December, Greece was rocked by the worst riots in decades following the police shooting of a teenager. A policeman was seriously wounded by unknown assailants last week and police say ballistic evidence links the shooting to Revolutionary Struggle.