By Daniel Flynn and Annika Breidthardt
The plan could see the banks take a 100 billion euro ($139 billion) hit that halves the book value of their holdings and includes a small "cashback" component to soften the blow.
It is the descendant of a proposal dating back to July and is aimed at forcing banks to share some of the cost of Europe's bail-out bills with taxpayers.
Greek Finance Minister Evangelos Venizelos said banks and insurers would receive 15 euros in cash and 35 euros in 30-year, 6-percent coupon bonds for every 100 euros of debt they own, according to Greek newspaper Kathimerini.
The talks are aimed at preventing a Greek default -- which would trigger an auction of the Credit Default Swaps (CDS), a hard-to-predict event that could cause chaos in markets -- by persuading the banks to take the cuts voluntarily.
The Venizelos proposal would indicate a write-off of 58 to 61 percent in so-called net present value (NPV) terms, an estimate of the value of future interest payments minus the risk of holding the Greek bonds for the next 30 years.
Some bankers still balk at the idea.
"That was the opening gambit from the official sector a while ago. It's too harsh in my mind. Investors will prefer to take their chances in the CDS auction," said one banking source, in a reference to the risk of a disorderly default.
In a key difference from July's restructuring proposal, the new bonds issued would not have a guarantee from the European Financial Stability Facility (EFSF), banking sources said. The cash payment would act as an incentive instead.
The banks -- grouped together in the International Institute for Finance (IIF) lobby -- had proposed a mere 40 percent cut, with huge guarantees in the form of collateral, according to a senior government source involved in the talks.
But that offer was not good enough, the source said, and two other banking sources said they were now inching closer to a deal that would see a 50 percent cut in NPV.
"Politically they can't afford not to deliver, and they don't have the courage to cause a Lehman-style event," one of the banking sources said.
Banking sources said that support for a cash element alongside a bigger loss was gaining support, but that the terms of any deal and the proportions of cash and bonds could still change and result in different levels of haircut.
"The details of the final proposal and the alternatives that it will include will be finalized in the coming days," said one senior banking source.
Hopes that European Union leaders will deliver a comprehensive deal on Wednesday to solve Europe's debt crisis once and for all are fading, as several key components of the package are still being debated.
They are in broad agreement on the need to recapitalize Europe's banks by 100-110 billion euros, but are not expected to agree a final plan for Greece, or on how to boost the firing power of Europe's EFSF bailout fund.
In her latest comments, German Chancellor Angela Merkel said the goal of talks must be to cut Greece's debt to 120 percent of Gross Domestic Product by 2020, which would imply a 50 percent haircut on bonds, according to EU analysis.
Bondholders face losses of 60 percent if Greece's debt mountain is to be reduced to 110 percent of GDP, according to a report by the European Commission, the European Central Bank and the International Monetary Fund this week.
There are 206 billion euros of Greek government bonds in private sector hands, so a 50 percent haircut would see banks take a 103 billion hit. Greek companies hold an estimated 80 billion euros, including 45-50 billion by its banks.
Those banks hurt by the haircut could need about 30 billion euros of capital from the state to shore them up as part of a recapitalization plan alongside the Greek debt talks, reducing the net benefit to Greece to nearer 70 billion euros.
The private sector agreed in July to take a mere 21 percent loss on their holdings of Greek debt, but the outlook has since deteriorated and they have been told they need to take a bigger loss to put Greece on a more sustainable path.
($1 = 0.719 Euros)
(Additional reporting by Harry Papachristou, Tatiana Fragou, Lefteris Papadimas, Edward Taylor, Alex Chambers and Steve Slater; Editing by Douwe Miedema and Andrew Callus)