Migrants are currently sleeping in waiting halls normally used by ferry passengers and in more than 1,000 camping tents put up in the docks.
But they say they are reluctant to register in official camps out of fear to get stranded there.
A woman who said that she was in a camp near Larissa, 250 kilometres to the north, told Skai TV in Piraeus that conditions in the regulated facilities were miserable.
Meanwhile, the authorities began planning another camp for 6,300 people on a military compound near the capital in a bid to ease the pressure on Piraeus.
Overall, Greece intends to expand the sheltering capacity by another 30,000 places in the coming weeks, as a resettlement mechanism the European Union agreed with Turkey is due to gain momentum.
Shortly before the returns begin, nerves are running raw in the camps, the Athens daily Kathimerini reported Wednesday.
"Kill us here, but don't send us back to Turkey," read a message on a banner waved by migrants in Moria on the island of Lesbos.
Presently, more than 50,000 migrants are stranded in Greece, between Turkey and closed borders to the north.