"The holder of the passport passed through the island of Leros on Oct. 3, 2015, where he was identified according to EU rules," Greece's deputy minister in charge of police, Nikos Toskas, said in a statement.
Toskas did not know if the Syrian passport had been checked by other countries through which the holder might have passed on his way to France.
A Greek police source said the passport's owner was a young man who had arrived in Leros on a small vessel from Turkey with a group of 69 refugees and had his fingerprints taken by Greek officials.
Following the Paris bloodshed, populist leaders around Europe rushed to demand an end to an influx of refugees and migrants from the Middle East and Africa. Poland said it cannot accept migrants under EU quotas without security guarantees.
If one or more of the attackers turn out to have come into Europe amongst the migrants arriving from war-torn countries this could change the political and security debate about refugees and what to do with them.
Police declined to give the name of the Syrian passport holder, saying French authorities wanted to keep information about the suspect confidential.
The source said there were no official records showing the man had left Greece, but that authorities believed he may have done so through the border with Macedonia.
Greek police were also asked by French authorities to check on the holder of an Egyptian passport that was apparently found near the body of another attacker, but found no evidence so far that this second person may have also passed through Greece, the police source said.
Greece has seen about 600,000 refugees and migrants - mainly from Syria, Afghanistan and Iraq - arrive on its shores this year, mostly from nearby Turkey, hoping to reach wealthier northern Europe.
Leros island, in the southern Aegean sea, is one of five preferred entry points where Greek authorities have been setting up so-called hotspots to register and identify arrivals.
(Reporting by Renee Maltezou and George Georgiopoulos, writing by Silvia Aloisi, Editing by Clelia Oziel)