Turkey may still appeal the case, and any final decision to extradite rests with the Greek minister of justice
The court reasoned that the three men -- out of a total eight officers seeking asylum in Greece -- faced threats to their personal safety if returned to Turkey.
It also deemed that Turkish authorities have not provided sufficient evidence tying them to the coup attempt against President Recep Tayyip Erdogan, the source said.
The court is expected to decide the fate of the other five officers on Tuesday.
Turkey may still appeal the case, and any final decision to extradite rests with the Greek minister of justice.
The two Turkish commanders, four captains and two sergeants requested asylum in Greece after landing a military helicopter in the northern city of Alexandroupoli shortly after the attempted government takeover in mid-July.
The officers are currently appealing against a Greek refusal to grant them asylum in September.
Ankara has asked Athens to extradite them all to face trial in Turkey for their alleged role in the failed coup, including an alleged attempt on Erdogan's life.
The officers say they would not receive a fair trial in Turkey, where the authorities have detained thousands of people over the coup, including top generals.
Their lawyer Stavroula Tomara said the "humiliating" treatment and "torture" meted out to other coup suspects in Turkey had made an impression on the Greek court.
The case is awkward for Greece, which depends on Turkey to stem the flow of tens of thousands of migrants to its shores.
Several Turkish nationals, including civil servants and businessmen, have sought refuge in Greece following the coup attempt.
NATO chief Jens Stoltenberg last month said an unspecified number of Turkish officers serving in NATO command positions had requested asylum in those alliance member states following the botched coup on July 15.