Eurozone finance ministers meeting in Brussels have not ruled out giving Greece more time to pay back its debts.
However, they are expected to demand that Athens proceeds more quickly with the sale of state assets and with deeper economic reforms in return.
Ministers have suggested that private investors holding Greek debt could be asked to voluntarily extend the maturities on their bonds to allow Greece more time to pay back what is owed.
It is the first time there has been such a development in the EU bailout process.
Any such move would, however, be voluntary and would not be imposed.
The moves follow intense speculation that Greece will not be able to repay its €330bn debt and will, at some point, default.
However, the chairman of the eurogroup of countries which use the single currency, Luxembourg Prime Minister Jean-Claude Juncker, has said there is no question of Greece restructuring - or defaulting on - its debt.
Earlier, German Chancellor Angela Merkel spelt out strong opposition to any restructuring of debt, or default, within the eurozone.
She said that any such move before 2013, when a permanent rescue mechanism is put in place, would be 'incredibly' damaging to the euro as a whole.
The new mechanism, known as the European Stability Mechanism (ESM), is expected to require some burden sharing of bondholders.
Greece is thought to need an extra €60bn to meet its debt repayment requirements in 2012-13.
Most analysts argue that the €110bn bailout agreed last year will not be enough to meet those needs, especially since the Greek budget deficit level is higher than that foreseen within the EU-IMF rescue programme.
The Greek debt is expected to reach 160% of what the country earns by next year.
One well-placed source told RTÉ News that there was some anger expressed by ministers during yesterday's gathering that Greece was not meeting the terms of the rescue package, particularly in relation to the sale of public assets, worth an estimated €50bn.
