The European Central Bank is expected to say on Saturday that Greek's battered banks need up to 14 billion euros ($15.4 billion) in fresh capital in order to survive.
It comes after years of economic decline in Greece - bailed out three times by international lenders - that has forced some 42 billion euros to be set aside against bad loans.
Although the banks are currently been kept afloat by access to money through the euro zone monetary system, there is a rush to get recapitalisation completed.
If it is not done by the end of the year, new European Union rules mean large depositors such as companies may have to take a hit in their accounts.
The announcement, to be made at 9.30 a.m. GMT, follows to see how they are faring after the long-running dispute over reforms demanded of Greece for international support.
This bailout stand-off between leftist Prime Minister Alexis Tsipras and his country's international backers - the International Monetary Fund and European Union - almost saw Greece tumble out of the euro zone.
It led to the freezing of central bank funding for Greece's banks and forced controls on cash withdrawals. Although the latter helped stem a further hemorrhaging of savings, it squeezed the economy, making it harder for borrowers to repay loans.
Of a new 86-billion-euro bailout of Greece, 25 billion euros is earmarked .
The fact that the capital hole is smaller that this may encourage investors and limit the amount of cash that Athens has to spend in a bailout that tangles the state further in the ownership of the four big groups.
To reach their conclusion, the ECB's supervisors are set to count into their calculation roughly 12 billion euros of future tax rebates that the Greek government could pay its banks.
The assessment looked at how many loans would go unpaid if the country's economy performs as expected up until 2017 - the so-called 'baseline'. It will also simulate a 'stress' scenario, where the economy dips further. Under the baseline scenario, the stress test will show a capital gap of about 4.5 billion euros for the four banks, one banking source has told Reuters.
Adding the 'adverse' or stress scenario, the gap could be as high as roughly 14 billion euros.
Greek bankers hope that private investors will buy shares in the lenders. But Greece's future and that of its banks remains uncertain, despite the latest checks.
A fall of more than two thirds in the banks' stock prices this year has served as a reminder of the risks.
Greece on Friday put forward a bank recapitalisation bill that outlines how new funds will be pumped into the banks.