Talks have stalled between Greece and private sector lenders over a possible 50% debt write-off.
Reaching a deal over the 100 billion euros ($US126 billion) worth of debt is a pre-condition for Athens receiving the next tranche of bailout funds from the International Monetary Fund and European Union.
Without the money, the BBC reports the Greek government could run out of cash and be forced to leave the euro.
The alternative to a voluntary debt write-off is likely to be an outright default by Greece - a failure to continue repaying its debts.
Some of Greece's debts are reported to have been bought on the cheap by vulture funds - speculators who specialise in pursuing troubled borrowers for payment in full.
A common tactic of vulture funds is to veto agreements between distressed borrowers and their main lenders, in the hope of winning special treatment for their own loans.
The European Central Bank - which has bought a significant share of Greece's debts as part of efforts to rescue the country - is not participating in the talks and will not accept any write-off of the debts it holds.
The BBC reports Greek debts are currently valued at only 20% of face value by bond markets.
Greece has a rating equivalent to that of a partial default from Standard & Poor's at CC with negative outlook.