Joshua Kyller, co-ordinator of Catholic Relief Services' work in the Balkans, said that at the Piraeus Port in Greece around 5000 people are sleeping in empty warehouses because no other shelter is available.
Speaking to The Catholic Herald, he said: "I've never seen anything like it from a humanitarian standpoint."
"Many [migrants] are unsure about what will happen to them."
Migrants living in tents at a flooded field at the northern Greek border station of Idomeni.
On Tuesday the United Nations and a number of human rights groups voiced concerns about the European Union's plans to send thousands of migrants back to Turkey from Greece, amid fears the country cannot properly provide for them.
Around 40,000 people are thought to be stuck on the Greek border with Turkey after the Balkans Corridor - a route used by more than a million people so far - was closed.
A Syrian refugee woman tries to clean the mud from her clothes in an improvised camp on the border line between Macedonia and Serbia, near northern Macedonian.
Joshua Kyller added: "There is an emergency developing within the emergency of this growing mass of people coming in.
"Another emergency will happen when they technically become illegal. Will we be able to continue to provide food, water, shelter?"
EU and Turkish leaders have agreed to the broad outlines of a deal that would essentially outsource Europe's refugee emergency.
Migrants and refugees arriving in Greece would be sent back to Turkey unless they apply for asylum, and for every migrant sent back, the EU would take in one Syrian refugee.
They hope this will prevent the need for people to set out on dangerous sea journeys, often arranged by people smugglers.
But speaking on Tuesday Filippo Grandi, the UN High Commissioner for Refugees, said: "I am deeply concerned about any arrangement that would involve the blanket return of anyone from one country to another without spelling out the refugee protection safeguards."
