The boat is believed to have sunk Saturday off the coast of Sererihisar, south of the city of Izmir, Anatolia reported, quoting local governor Orhan Sefik Guldibi. Six of the migrants were rescued late Sunday.
Guldibi said rescuers had recovered 20 bodies that had washed ashore.
"The survivors said there were between 60 and 70 people on board. We are afraid that the death toll will rise," he told Anatolia.
There was no immediate information on the migrants' nationalities.
Thousands of immigrants from Asia and Africa enter Turkey illegally on their way to European countries in search of jobs and a better life.
Smugglers often take the migrants to Greece on fragile and overcrowded boats, and such accidents are not uncommon.
The European Union, which Turkey wants to join, is pressing Turkey to crack down on illegal immigration.
So Donald Trump referred to "shithole" countries in a meeting on immigration. Or did he? In denying the allegations, claiming that was "not the language used", while others state that was the language used, either he, or they, are lying. The bottom line is, what to make out of the "shithole incident"?