EU finance officials discussed options for resolving Greece's intractable debt crisis on Monday, galvanized by the growing threat of contagion to Italy, the euro zone's third-largest economy.

European Union sources told Reuters the Eurogroup of 17 euro zone finance ministers were discussing the possibility of buying back Greek debt or the private sector swapping holdings for longer-dated maturities in a move to make Greece's debt, which total more than 160 percent of GDP, more sustainable.

If so, it suggests a French plan that would have involved private sector creditors rolling over around 70 percent of their Greek debt into 30-year bonds and other AAA-rated securities is losing favor and other options are back under the microscope.

Germany, the Netherlands, Austria and Finland are determined that banks, insurers and other private holders of Greek government bonds should bear a chunk of the costs of a second Greek bailout, which is expected to total 110 billion euros.

But after weeks of negotiations with bankers, there has been next to no progress on agreeing a formula acceptable to all sides.

As the French plan has faltered, Berlin has revived a proposal to swap Greek bonds for longer-dated debt that would extend maturities by seven years. Proposals to buy back Greek bonds and retire them have also been floated.

We need to find a way to have some guidelines today on the private sector involvement and the solution for Greece, Belgian Finance Minister Didier Reynders told reporters. That's the real issue today, I'm sure.

One senior EU source said the Eurogroup would ask technical teams to focus attention on two options -- bond buybacks and a debt rollover.

There is a strong possibility that a new Eurogroup meeting will be called at the end of July, to sign off on the solutions, the source said.

Both those schemes would likely be regarded by ratings agencies as a default, or at best a selective default, which could have profound repercussions for global financial markets.

The European Central Bank insists it will not accept anything that is termed a default, a position Germany also holds, even if some policymakers may be edging closer to effectively condoning a default to achieve a write-down in the value of Greek debt to make its debt mountain more sustainable.

We do pursue a voluntary basis but it has to be substantial private sector involvement. That's our commitment and also our parliament that demands it, Dutch Finance Minister Jan Kees De Jager said.

In a buy-back, the bloc's European Financial Stability Facility (EFSF) bailout fund might buy Greek bonds from the market, or lend Greece money to do so. Officials say that would require changes to the EFSF's rules which would need the backing of national parliaments -- a further potential obstacle.

One senior EU official described the situation as now being almost entirely a political rather than an economic crisis, with parties taking firm, irreconcilable positions.

We've painted ourselves into a corner. At this point, either someone -- Germany, the ECB -- has to fundamentally shift position, or everything blows up, they said.

ITALY FOCUSING MINDS

Policymakers have been seized with a new sense of urgency after Italy came under market attack last week, fearing any further delay in putting together a second Greek package could poison investor confidence in weak economies around the region.

After talking by phone to Italy's Silvio Berlusconi, German Chancellor Angela Merkel said Rome needed to demonstrate it was undertaking the budget reforms needed to restore confidence and she was confident that it would do so.

Earlier, Herman Van Rompuy, the president of the European Council, met ECB President Jean-Claude Trichet and Jean-Claude Juncker, the chairman of the Eurogroup, for talks in Brussels ahead of the euro zone finance ministers' gathering.

Van Rompuy's spokesman described the meeting, which European Commission President Jose Manuel Barroso and EU economic and monetary affairs commissioner Olli Rehn also attended, as a coordination, not a crisis meeting.

He said Italy was not on the agenda but senior EU sources said it would be impossible not to discuss it following a large sell-off in bonds and stocks that the Italian media have dubbed black Friday.

The cost of insuring Italian debt against default jumped to a record high on Monday, the 10-year yield spread over German debt widened to a euro-era high of 300 basis points and bond yields rose above the 5.7 percent area which bankers say will start putting heavy pressure on Italy's finances.

The sell-off has increased fears that Italy, with the highest sovereign debt ratio relative to GDP in the euro zone after Greece, could be next to get dragged into crisis. If that came to pass, the euro zone's existing rescue mechanism, the EFSF, would have insufficient funds to help.

Austria's Finance Minister Markia Fekter said ministers wanted to quiz Italy about how it was handling the situation.

We have a Eurogroup meeting today and tomorrow Ecofin. We will (discuss) the IMF decisions and we will also have questions for the Italian minister there, she told reporters.

The market pressure is due in part to Italy's high sopromoted deep and sluggish economy, but also due to concern that Prime Minister Silvio Berlusconi may be trying to push out his long-time finance minister, Giulio Tremonti, who has promoted deep spending cuts to control the budget deficit.

We can't go on for many more days like Friday, a senior ECB official told Reuters. We're very worried about Italy.

German newspaper Die Welt quoted an unnamed ECB source assaying the EFSF may have to be doubled in size to 1.5 trillion euros if it is to be capable of coming to the aid of Italy.

(Additional reporting by John O'Donnell, Leigh Thomas and Luke Baker in Brussels, Silvia Westall in Vienna, Stephen Brown in Berlin and Milan/Rome bureaus, writing/editing by Mike Peacock)