Private investors would have to forgive 60 percent of what Greece owes them to make its debt sustainable by 2020 and for a eurozone loan package to stay at the 109 billion euros agreed in July, a report by international lenders said.

The confidential report, discussed by eurozone finance ministers on Friday, will form the basis for talks with private investors on what losses they should accept on their Greek portfolios in the second emergency financing plan for Greece.

Private investors have already offered to accept a net present value loss on their Greek portfolios of 21 percent under a deal struck with eurozone leaders in July.

But since then Greece turned out to be in a deeper-than-expected recession, it is behind on its structural reforms, privatisation and fiscal goals and market conditions have deteriorated.

Euro zone leaders therefore want to reopen the talks on how much private investors should contribute to keep Greece financed on top of cash from eurozone taxpayers. They are to make a decision on the private sector involvement (PSI) at a summit next Wednesday.

"Deeper PSI, which is now being contemplated, also has a vital role in establishing the sustainability of Greece's debt, said the report by experts from the European Commission, the International Monetary Fund and the European Central Bank.

The report analyses scenarios using discount bonds with an assumed yield of 6 percent and no collateral to assess the potential magnitude of improvements in the debt trajectory and potential implications for official financing.

"Debt can be brought to just above 120 percent of GDP by end-2020 if 50 percent discounts are applied," it said.

"Given still-delayed market access, large scale additional official financing requirements would remain, estimated at some 114bn euros (under the market access assumptions used)," the report said.

"To get the debt down further would require a larger private sector contribution (for instance, to reduce debt below 110 percent of GDP by 2020 would require a face value reduction of at least 60 percent and/or more concessional official sector financing terms)," it added.

"Additional official financing requirements could be reduced to an estimated 109bn euros in this instance," it said.

The report said that if the 21 percent net present value loss were to be maintained under the changed conditions, the cumulative additional financing needs from the eurozone, beyond what remains undisbursed in the present programme, and including the eventual rollover of existing official loans, could amount to some 252bn euros through to 2020.

This would still only lower the Greek debt to GDP ration to 152 percent in 2020 from an expected peak of 186 percent/GDP in 2013.