The coast guard said that "their craft rammed into a rocky location and sank." A Greek naval helicopter and one coast guard vessel are en route to the scene.
Additional details about potential casualties or the nationalities of the migrants were not known to the coast guard.
In front of the Peloponnese peninsula's southeasterly most point sits the island of Kythera.
In 2015 and 2016, when one million migrants from conflict and poverty in Syria, Iraq, and Afghanistan entered, mainly via Turkey, Greece was at the centre of Europe's migration crisis.
The number of migrant arrivals has fallen sharply since but attempts to enter the country by sea through its islands continue.