"The government is aware of 136 asylum applications filed by diplomatic passport holders from Turkey. They also include family members," said the interior ministry in a written reply to a query from a lawmaker.
The ministry said however that it did not have data on how many among the applicants are diplomats and how many are soldiers stationed at NATO bases.
President Recep Tayyip Erdogan's government has accused US-based Islamic preacher Fethullah Gulen of having orchestrated the putsch, and launched a sweeping crackdown against his followers.
Some 43,000 people in Turkey have been arrested over their suspected links to Gulen's movement, and 100,000 fired or suspended. Many of them are teachers, police, magistrates and journalists.
The scale of the crackdown has raised international concern, with Germany among the most vocal in raising questions over the mass arrests.
That and a string of other spats have contributed to fraying ties between Ankara and Berlin.
Turkey has also been pushing for Berlin to extradite alleged supporters of Gulen and PKK militants.
In its written note, the interior ministry said it extradited 60 people back to Turkey in 2015 for various offences including terrorism and murder.
Data for 2016 would only be available in 2018, it added.