Eight of the 11 dead were children, the media outlet added.
The boat sank on Saturday in the Aegean Sea near the city of Cesme in the province of Izmir.
Turkey is one of the main transit points for migrants and refugees seeking a way into Europe after fleeing war and persecution. The country itself hosts up to 3.6 million Syrian refugees.
In recent months, migration via Turkey has reached its highest levels since an EU-Turkey deal was sealed in 2016. According to the deal, Ankara promised to prevent migrants from reaching Europe through its territory in return for considerable financial assistance.