Greece faces a critical 24 hours as European leaders gather for an emergency summit in Brussels that could break the deadlock around the country’s debt crisis.
On Sunday, Greek PM Alexis Tsipras set out new proposals to try to prevent a default on a €1.6bn (£1.1bn) IMF loan.
One European official said the proposals held plenty of promise.
Greece must repay the loan by the end of June or risk crashing out of the single currency and possibly the EU.
Talks have been in deadlock for five months. The European Commission, the IMF and the European Central Bank (ECB) are unwilling to unlock the final €7.2bn tranche of bailout funds until Greece agrees to economic reforms.
The three creditors must agree to the deal offered by Greece to ensure Monday’s talks have a clear focus.
Analysis – Robert Peston, BBC economics editor
If deposit withdrawals continue at the current pace, Greek banks will soon exhaust eligible assets they can pledge to the Bank of Greece for cash under the Emergency Liquidity Assistance (ELA) scheme.
Even before that, the European Central Bank could turn off the ELA drip feed – because it is forbidden to allow the Bank of Greece to lend to insolvent banks.
If Greece’s bailout talks collapse, it would be hard for the ECB to maintain the fiction that the Greek banking system is solvent – given that the value of a big chunk of banks’ assets depends on the solvency of the Greek state.
So the ECB would have to take the banks off life support.
And the Greek authorities would have no realistic option but to impose capital controls, or restrictions on how much cash can be withdrawn by customers from the banks.
Prime Minister Tsipras is meeting the heads of Greece’s three international creditors at 11:00 (09:00 GMT), ahead of his talks with the leaders of 18 other eurozone nations.
Mr Tsipras’ offer on Sunday of a reforms package to the leaders of Germany, France and the European Commission is seen by some as a sign the Greek government is willing to make concessions.
The proposals, which Mr Tsipras described as “mutually beneficial”, were adopted at an emergency meeting of the Greek cabinet – though they have yet to be revealed.
The ECB will also hold a separate meeting on Monday to decide whether to raise the level of emergency funding for Greek banks, after it approved an emergency loan on Friday.
Greek savers have withdrawn billions of euros in recent days, putting Greece’s banking system under intense pressure.
Thousands of demonstrators gathered in Athens on Sunday evening in support of its left-wing government, which came to power off the back of an anti-austerity promise.