As of next week, Greek liaison officers will be stationed at airports in Frankfurt and Munich to help with passport checks, the source said.
The move follows a complaint by Germany's interior ministry that between January and October, around 1,000 people with falsified documents were intercepted at German airports after flying in from Greece.
Another two cases were found this week, the Kathimerini newspaper reported Thursday.
Greek police regularly crack down on forgery gangs, mainly based in Athens, which supply false passports to asylum seekers trying to leave the country.
But in recent days, German airport police have stepped up checks even on German citizens returning from Greek vacations, the police source said.
"They are even opening luggage. We heard of one person delayed for one and a half hours," the source said.
The source also said German authorities had not given Greece any specific details on the hundreds allegedly found carrying false papers over the past 10 months, which could have enabled Athens to run background checks on them.
German media reports have recently accused Greece - which has struggled to accommodate the estimated 60,000 refugees and migrants on its territory for the past year - of turning a blind eye to asylum seekers sneaking out.
The Greek migration ministry has strongly denied the reports.
Germany is a top destination for thousands of refugees and migrants trapped in Greece since a succession of European states shut their borders last year.
Even people granted refugee status by Greece have faced long delays in securing permission from German authorities to legally join their families.