The Black Hawk chopper arrived after sending a distress signal to authorities at the airport in Alexandroupolis in the country's north.
Seven of those on board were in military uniform and all are believed to have been involved in the attempted putsch, ERT TV said.
Athens News Agency said the asylum seekers comprised three majors, three captains and two sergeant majors.
Turkey's Foreign Minister Mevlut Cavusoglu said Ankara had asked Athens to send back the eight.
"We have requested Greece to extradite the eight traitors as soon possible," Cavusoglu was quoted as telling HaberTurk television.
According to an official in the Greek National Defence General Staff, "the helicopter is scheduled to be sent back immediately to Turkey".
"As far as the asylum seekers are concerned, we are going to proceed according to the international law" Olga Gerovassili, the Greek government spokeswoman, said.
She said Athens was "in constant contact with the Turkish authorities", and would take into account the fact that "the asylum seekers took part in a coup against the Turkish constitution".
Greek Prime Minister Alexis Tsipras early Saturday expressed his "support for the democratically elected" Turkish government.