(REUTERS) -- Eurozone finance ministers will decide on Monday what terms of a Greek debt restructuring they are ready to accept as part of a second bailout package for Athens after negotiators for private creditors said they could not improve their offer.

Resolving the issue of a Greek debt swap is key to putting Athens' debt on a sustainable path and avoiding a chaotic default that could threaten the whole currency bloc.

After several rounds of talks, Greece and its private creditors are converging on a deal in which private bondholders would take a real loss of 65 to 70 percent on their Greek bonds, officials close to the negotiations said.

But some details of the debt restructuring, which will involve swapping existing Greek bonds for new, longer-term bonds to bring Greek debt down to a more sustainable 120 percent of GDP in 2020 from 160 percent now, are unresolved.

What I am confident of is that our offer, that was delivered to the prime minister, is the maximum offer consistent with a voluntary PSI deal, Institute of International Finance chief Charles Dallara, who is negotiating on behalf of banks and insurers holding Greek debt, told Antenna TV on Sunday.

We are at a crossroads and I remain quite hopeful, said Dallara, who left Athens on Saturday without a deal in place.

Once the guidance from the finance ministers, known as the Eurogroup, is clear, talks on the restructuring could be finalized later in the week.

It is a very delicate moment, Greek government spokesman Pantelis Kapsis told Greek state radio.

The only thing that I can say as a government spokesman is that tonight, there is a very important meeting at the Eurogroup and we hope that serious steps will be made towards a deal.

Talks on the extent of Private Sector Involvement (PSI) in the Greek debt restructuring are a vital part of a second financing plan for Athens that would keep it funded until 2014.

We will listen to the report on the negotiations, see how far they have gotten and have the ministers say what is acceptable and what is not in terms of outcome of the negotiations, one Eurogroup official said.

Without the second bailout from the Eurozone and the International Monetary Fund, Greece will not be able to pay back 14.5 billion euros in maturing bonds in March, triggering a messy default that would hurt the whole Eurozone economy.

We are working for a deal in time for the Jan. 30 summit of EU leaders. The restructuring offer needs to be made in the course of February, the official said.

Obviously there is a clear link between the PSI and the next program and what we will be focusing on in the Eurogroup is making the next program operational.

STICKING POINT

There are doubts that even with a new bailout Greece's mountainous debt can be reduced to a still-painful 120 percent of GDP by 2020.

German Finance Minister Wolfgang Schaeuble said on Sunday the crucial factor was that Athens should have a level of debt that was sustainable by then. This goal must be achieved, he told German public broadcaster ARD.

Eurozone leaders agreed in October that the second bailout would total 130 billion euros, if private bondholders forgave half of what Greece owes them in nominal terms.

But Greek economic prospects have deteriorated since then, which means either Eurozone governments or investors will have to contribute more than thought.

The main sticking point is coupon, or interest rate, the new Greek bonds would carry. Officials said the new bonds are likely to be 30 years in maturity and carry a progressively higher coupon, which would average out at around 4 percent.

The Eurozone ministers will examine the proposal and say whether we have a deal. If they say we don't, we're back to the negotiating table, a banking source close to the talks said.

Progress will be presented to Euroz one ministers by Greek Finance Minister Evangelos Venizelos. We then expect a discussion about the coupon, a senior Greek banker close to the negotiations told Reuters.

I believe that the private sector can accept a lower coupon than the 4 percent average, but the question then is: will the PSI still be on a voluntary basis? he said.

The voluntary character of the debt restructuring is important to avoid triggering the pay-out of insurance against a Greek default.

While the sums of such insurance appear relatively small, Eurozone officials said, such a credit event could trigger a chain reaction of events that would entail rapid and large scale contagion in Eurozone debt markets, and is thus best avoided.

NEW RESCUE FUND

After dealing with Greece, Eurozone ministers will choose a replacement for European Central Bank Board member Jose Manuel Gonzales Paramo, whose term ends in May.

The 17 ministers of the Eurozone will then be joined by 10 ministers from the other European Union countries to finalize a treaty setting up the Eurozone's permanent bailout fund - the 500 billion euro European Stability Mechanism (ESM). Its predecessor, the EFSF, is widely viewed as insufficient.

The ESM is another crucial element in the bloc's efforts to end the sovereign debt crisis that threatens to engulf Spain and Italy after claiming Greece, Ireland and Portugal.

The fund should boost market confidence in Eurozone defenses should Spain or Italy need emergency financing. Separately, the IMF has launched a proposal to boost its war chest by $600 billion.

IMF head Christine Lagarde is to discuss this during a meeting with German Chancellor Angela Merkel on Sunday. She will make a speech on Monday in which she is expected to urge Eurozone leaders to act quickly while acknowledging it is not merely Europe's problem because innocent bystanders will also be hit by a worsening debt crisis.

The 27 EU finance ministers will also prepare the final draft of another treaty to sharply tighten fiscal discipline in the Eurozone, called the fiscal compact, that is designed to ensure another sovereign debt crisis cannot happen in future.

EU leaders are to sign off on both treaties on Jan. 30, allowing the ESM to become operational in July.

To prepare for the Jan. 30 summit, Merkel will meet European Commission President Jose Manuel Barroso and European Council President Herman Van Rompuy on Monday evening.

(Additional reporting by Lefteris Papadimas and Ingrid Melander in Athens; Reporting By Jan Strupczewski, editing by Mike Peacock)