French President Nicolas Sarkozy says his country's banks would help Greece by giving it 30 years to repay.
France's Figaro newspaper said banks are ready to relend - or roll over - 70% of loans they hold.
The plan is being worked out by the French government and bankers.
Greece, which has not yet exhausted all its first 110bn-euro (£98bn, $158bn) bail-out, is already standing by for further rescue loans expected to be up to 120bn euros.
Losses
However, the German government and others have been pressing for banks and other private-sector lenders to Greece to be involved this time round.
German banks are reported to be very interested in the French model being discussed.
A group of international bankers are currently meeting eurozone officials in Rome to discuss the crisis.
The matter is fraught because credit rating agencies, who determine the credit-worthiness of borrowers, have already said they will view any roll-over of loans by banks as a technical default, something that is tantamount to bankruptcy.