The boss of Italy's biggest bank says Europe's banks can work together with European institutions to help Greece."I think there is room for strong collaboration," said Corrado Passera, chief executive of Intesa Sanpaolo.
On Monday, French President Nicolas Sarkozy said French banks had agreed to extend their loans to Greece.
Eurozone officials are trying to find a way for banks to support Greece's bail-out without the country being judged to have defaulted on its debt.
Credit ratings agencies have warned that if banks agree to extend their loans to Greece, even voluntarily, they may judge it to be a debt default, which would cause even more problems for Greece.
President Sarkozy's idea was that when banks are repaid money they are owed by Greece, they should keep 30% of it, re-lend 50% of it to Greece for 30 years and put the remaining 20% into a special fund of high-quality bonds, which would insure them against a future Greek debt default.
French banks have the biggest exposure to Greek debt, while Italy has relatively low exposure.
The deal may be unpopular with Germany, because the new bonds would be insured by eurozone bail-out funds.
The French plan has yet to be agreed either with eurozone leaders or the Greek government.BBC business editor Robert Peston says the real problem with the proposals is that there has been no attempt to reduce the amount of money that Greece owns, unlike in the Brady bonds for indebted countries such as Mexico, Argentina and Brazil, on which President Sarkozy's plans were based.
Nonetheless, German banks are reported to be very interested in the French model being discussed.
They were discussed by a group of international bankers, who met eurozone officials to discuss the crisis on Monday.
Also, the head of the eurozone's rescue fund, Klaus Regling, is talking to the ratings agencies to explore ways to avoid a second bail-out being considered a default.
European policymakers, notably the European Central Bank, are concerned that the bail-out could force European banks to recognise billions of euros in losses on Greek debts they currently hold, and could also trigger payouts on credit derivative contracts.
Credit derivative contracts are, in this case, bets that Greece will default on its debt. They are used partly as insurance by banks that have bought Greek bonds.
The Greek parliament is discussing a new range of austerity measures, which include introducing income tax on earnings of 8,000 euros (£7,142, $11,600), and is due to vote on the package later in the week.
The ruling party has 155 seats in a 300-seat parliament. Polls suggest the proposals are opposed by three quarters of Greece's 11 million population.
The austerity measures must be agreed before Greece can get its hands on the latest slice of the original 110bn euro support package.