Greek banks need state aid to get through the losses of a planned write-down of the country's sovereign debt but the lenders are pressing the government not to take over management at the same time.
Under a second debt rescue agreed in October with the EU and IMF, private creditors agreed to write-down 50 percent of their holdings of government bonds, effectively cutting Greek's debt burden by 100 billion euros.
The accord also made available 30 billion euros to help the Greek banks cope with the resulting losses on their holdings of Greek government bonds, put at around 50 billion euros, and which they could not cover themselves.
The aim of the 30 billion euros lifeline is to keep the banks alive and lending so that the Greek economy, mired in recession since 2008, is not deprived of essential credit to drive new business.
Complicating their position is the fact that they are already short on their provisions for bad loans, put at 12.8 percent of total lending according to June figures, meaning that they need even more fresh capital.
Finance Minister Evangelos Venizelos said recently that the Greek banks needed at least 40 billion euros to keep them afloat.
If the controversial bond write-down goes through, the banks would inevitably end up under control of the Greek government which in turn is now under the watch of the EU and International Monetary Fund as it pushes through tough austerity measures to stabilise the public finances.
"It is a question of principle," Venizelos said, adding that in practice the banks "will remain private ... and operate according to the rules of the private sector."
The banks, however, see the situation very differently, fearing that their existing shareholders will have their holdings badly diluted as the government in effect buys up their ordinary shares in return for funding.
To avoid that, they want the government to take preference shares, whose terms could be varied to limit their voting rights or the total stake they represent.
The recapitalisation of the banks "ought in principle be open to private investors, which does not mean that the state cannot take part but it is necessary that the conditions be clear and do not harm the private sector," said one Greek banker who asked not to be named.
The banks "invested hugely in (Greek) government bonds because at the time, they were the most reliable assets ... they did not invest in toxic assets," the banker said, referring to the disastrous US mortgage investments whose failure sparked the global financial crisis in 2008.
"Nobody has any confidence in the government to manage the banks. Its record on that count is disastrous," said Miranda Xafa of IJ Partners, an investment advice group.
Greek banks are also reluctant to cede control to the government given that many are closely held by some of the country's most important family business groups who have interests across the economy.
For example, the Latsis family, the richest in Greece, holds 44.6 percent of Eurobank while Yannis Kostopoulos holds 10 percent of Alpha Bank, its partner in a merger to be completed later this year.
Some analysts think however that the banks have had their own way too long, abusing their advantages in Greece to their own benefit and so government intervention might prove a good thing in the long run.
"These bankers are (also) businessmen who have their money in bank shares," said Stilianos Padelidakis at Primexis, an French-based accounting firm, charging that they play an active political role.
It would be healthy if the government cleaned up the banks "which have brought the country to its knees" by cutting off credit, Padelidakis said.