Europe may cut off its emergency loans to Greece which is keeping the country's banking system afloat.
The ECB is expected to meet today to decide the next steps for Greece’s financial lifeline following the decision by Greek Prime Minister Alexis Tsipras to hold a referendum on new bailout terms.
The referendum is due to be held on 5 July, days after the country’s debt default deadline expires meaning it will no longer be part of any bailout programme.
ECB President Mario Draghi and the bank’s governing council face a decision on whether to continue providing assistance to the country after the referendum move which has left talks between Eurogroup ministers and Greece in tatters.
Greece will likely have to "announce a bank holiday on Monday, pending the introduction of capital controls" the BBC’s Robert Peston reports.
The ECB’s ELA has been a lifeline for Greek banks, providing around €89bn in liquidity to the Greek economy.
Greece would likely have to introduce capital controls, restricting cash withdrawals from banks in order to prevent a run on them by Greeks wanting to get their hands on their cash.
People have already been lining up to withdraw money from cash machines in the country as the risk of its potential exit from the Eurozone looms.
More than a third of Greece's cash machines ran out of cash on Saturday before being replenished, Reuters reports, with estimates of more than €500m of cash being withdrawn from the Greek banking system.
Meanwhile, French Prime Minister Manuel Valls said the ECB should not cut off its support for Greece.
"The European Central Bank is independent, but I don't doubt it will assume its responsibilities. I don't think it can cut off support, to put it another way," he said in an interview with French media on Sunday morning. "I cannot resign myself to Greece leaving the Eurozone ... We must find a solution," he said.