After muddling through round after round of inconclusive talks, the negotiations are in their final phase - though it appeared unlikely that a preliminary deal would be secured in time for a European Union summit on Monday.

Greek bondholders said the two sides were finalising a deal along the lines of a proposal made by Jean-Claude Juncker, the chairman of euro zone finance ministers.

The bondholders' comments suggested creditors had accepted Juncker's demand for a coupon, or interest rate, of below 4 percent on new, longer-dated bonds that Athens will swap for existing debt.

The coupon had been the main stumbling block in the talks, with euro zone ministers rejecting private creditors' demand for a coupon of at least 4 percent - above the 3.5 percent level Greece and its European partners had been holding out for.

"Next week we will be in a position to complete the debt swap," Finance Minister Evangelos Venizelos said, citing significant progress at Saturday's talks. "We are really one step away from the final deal."

He confirmed that the two sides were working along the "exact framework" provided by euro zone finance ministers.

Charles Dallara, chief of the Institute of International Finance that negotiates on behalf of banks and insurers, is due to leave Athens on Sunday but will remain in contact with Greek authorities, the IIF said.

Still, for Athens, progress on the debt swap is at risk of being overshadowed by increasingly problematic talks with its foreign lenders, whose inspectors are in town demanding unpopular reforms that no politician wants to be linked to.

DENSE, DIFFICULT AND CRUCIAL

Crushed by 350 billion euros of debt and running out of cash quickly, Greece is scrambling to appease the "troika" of its official lenders - the European Commission, European Central Bank and International Monetary Fund - and stitch up a deal with private creditors simultaneously.

Unimpressed with Athens dragging its feet on reforms, the troika has said they could hold up aid if more is not done to make the Greek economy more efficient.

"It's all very dense, difficult and crucial," a Greek finance ministry official said.

European paymaster Germany is pushing for Athens to relinquish control over its budget policy to European institutions as part of discussions over a second rescue package, a European source told Reuters.

With many Greeks blaming Germans for the austerity medicine their country has been forced to swallow, officials in Athens dismissed the idea as out of the question. "The government stresses that this responsibility belongs exclusively to the Greek government," said government spokesman Pantelis Kapsis.

"The government has made a series of steps to improve the effectiveness of the public administration and a closer monitoring of the efforts to achieve fiscal targets.."

The European Commission, the executive arm of the 27-country bloc, said it wanted the Greek government to maintain autonomy.

"The Commission is committed to further reinforcing its monitoring capacity and is currently developing its capacity on the ground," a spokesman said. "But executive tasks must remain the full responsibility of the Greek Government, which is accountable before its citizens and its institutions. That responsibility lies on their shoulders and it must remain so."

A government source in Berlin said Germany's proposal was aimed not just at Greece but also at other struggling euro zone members which receive aid and are unable to make good on their obligations. "All options can obviously be introduced only with the agreement of, for example, the Greeks themselves," he added.

NEW BONDS FOR OLD

The debt swap, in which private creditors take a 50 percent cut in the nominal value of their Greek holdings in exchange for cash and new bonds, is also a prerequisite for the country to secure a 130-billion-euro rescue plan drawn up last year.

The two sides have broadly agreed that new bonds under the swap would have a 30-year maturity, but the talks ran into trouble over the coupon and whether the ECB and other public creditors must take losses on their holdings.

A deal, aimed at chopping 100 billion euros off Greece's debt load, must be sealed in about three weeks at the latest as Greece has to repay 14.5 billion euros of debt on March 20.

Otherwise Greece could sink into an uncontrolled default that might spread turmoil across the euro zone and tip the global economy back into recession.

IMF Managing Director Christine Lagarde said on Saturday that euro zone members were making progress to overcome their crisis but must do more to strengthen their financial firewall to stop the crisis spreading, adding the IMF was ready to help.

"There is progress as we see it," Lagarde told a panel discussion at the World Economic Forum in Davos.

"But it is critical that the euro zone members actually develop a clear, simple, firewall that can operate both to limit the contagion and to provide this sort of act of trust in the euro zone so that the financing needs of that zone can actually be met."

Concern has also grown in recent days that the debt swap may not do enough to get the country's debt reduction plan back on track, and that Greece's European partners will be forced to stump up funds to cover the shortfall.

The German news magazine Der Spiegel reported on Saturday that Greece's international lenders thought Athens would need 145 billion euros of public money from the euro zone for its second bailout, rather than the planned 130 billion euros.

The magazine said the extra money was needed because of the deteriorating economic situation in Greece, echoing a Reuters report on Thursday.

Greece is in its fifth year of recession, and hopes of an end to the crisis in the near term have virtually gone, because of the combination of squabbling politicians, rising social anger and its inability to push through badly needed reforms.

(Additional reporting by Andreas Rinke in Berlin and John O'Donnell in Brussels, Writing by Deepa Babington; Editing by Tim Pearce and Janet Lawrence)

• A Permanent Economic Emergency