Greek Finance Minister Yanis Varoufakis listens to International Monetary Fund (IMF) Managing Director Christine Lagarde (R) during an euro zone finance ministers meeting in Luxembourg, June 18, 2015. REUTERS/Francois Lenoir
A Greek banking official said the precise sum of the new credit will not be announced.
"The Greek banking system has no financing problems, and central bankers are looking to a positive outcome" during Monday's meetings on Greece, said the official.
Uncertainty has grown after a meeting about the economic reforms Greece must make to get more loans ended in acrimony.
Greece has a debt payment on June 30 it cannot afford and a default could eventually see it drop out of the euro.
Several European countries are now openly saying they are getting ready for such a possibility.
In the streets of Athens, there were no visible signs of distress or larger than usual lines at banks or supermarkets. Officials, however, highlighted an increase in withdrawals and transfers, which can also be made electronically.
An EU official said Greeks had taken about two billion euro (£1.4 billion) out of their accounts in the last three days.
"Money is going out of the Greek banks faster than at any time before," said the official.
The ECB has been steadily increasing the support it allows Greek banks to draw on, having done so just two days ago. It is not thought it would turn off that tap until it thinks Greece is definitely going bust, and certainly not before an emergency summit of the eurozone's 19 leaders on Monday.
However, if no deal emerges with creditors soon that will allow the country to pay upcoming debt payments, starting with one at the end of the month, the ECB would be under intense pressure to stop pumping money into a banking system that might collapse.
The creditors want Greece to agree to new reforms and a tighter budget before they give it more loans. Greece's radical left-led government, on the other hand, came to power in January on the promise to end such measures, which may have helped tame the budget deficit but have also increased poverty and unemployment.
Time is running out - Greece has to pay 1.6 billion euro (£1.15 billion) to the International Monetary Fund on June 30. It cannot afford that without a deal that would unlock 7.2 billion euro (£5.15 billion) in bailout loans.
Relations between the sides have soured in recent days, with each side blaming each other in increasingly strident language.
Around Greece on Friday, newspaper headlines warned time was running out. The daily Ethnos called Monday's summit the "Last Chance for a Deal" while the pro-government Efimerida ton Syntakton said creditors had put a "Knife to our Throat".
Greek prime minister Alexis Tsipras, who is due to meet Russian president Vladimir Putin in St Petersburg later following the signing of a gas deal between the two countries, sought to portray the events in a good light.
He said Monday's summit is "a positive development on the road to agreement," claiming that those "who invest in crisis and horror scenarios will be proven wrong".
Mr Tsipras added: "We sought final negotiations to be at the highest political level in Europe and now we are working for the success of this summit."
The Bank of Greece, meanwhile, said "the gap between Greece and its creditors is not a large one."
As finance ministers from across the 28-country European Union wrapped up talks in Luxembourg on Friday, there was barely hope that technical talks will resume over the weekend before eurozone finance ministers meet again on Monday ahead of the leaders' summit later in the day.
"We are a little sceptical that we will be able to prepare a great deal more than today," German finance minister Wolfgang Schaeuble said.
"But maybe the readiness in Greece to do what is necessary will increase over the weekend. The ball is in Greece's court.
"I'm not so sure that I will be able to announce sensational news to you on Monday."
It is not just eurozone countries that would be affected by a Greek exit from the euro. Some in the markets think a so-called Grexit could be another "Lehman Brothers" moment for the world economy - sparking a potentially destabilising chain reaction, the way the collapse of the investment bank did in 2008.
Others say it would be manageable, though the uncertainties are great.
Slovakia's prime minister, Robert Fico, said his country was "mentally and technically prepared" for a Greek euro exit. "We wish for Greece to remain in the eurozone, but not at all costs."
Investors appeared to take developments in stride, with the Stoxx 50 index of leading European shares up 0.6%. The main stock market in Athens was down just 0.3% in mid-afternoon trading. The yields on Greek government bonds fell, a sign investors think a deal is near.