The outline of a large and ambitious eurozone rescue plan is taking shape, reports from the International Monetary Fund (IMF) in Washington suggest.
It is expected to involve a 50% write-down of Greece's massive government debt, the BBC's business editor Robert Peston says.
The plan also envisages an increase in the size of the European Union bailout fund to 2tn euros (£1.7tn; $2.7tn).
European governments hope to have the plan in place in five to six weeks.
Turning the present outline into a practical reality will be immensely difficult, our editor says.
But he adds that the price of failure could be a financial crisis that would probably turn anaemic growth into a recession or worse.
Investors have so far been unimpressed with the speed at which policymakers have dealt with the eurozone debt crisis, and analysts say that action, not words, are needed to calm volatile stock markets.
Over the weekend, the G20 reasserted its commitment to "a strong and co-ordinated international response" to the crisis, but analysts warned this would not be enough to satisfy investors.
"Given that there were no details on how [the G20 would combat the crisis], it will not do much to alleviate market stress without some concrete action," said Mitul Kotecha at Credit Agricole.
Asian shares fell on Monday, with Japan's Nikkei index down 2.2%, Hong Kong's Hang Seng falling 2.4% and South Korea's Kospi losing 2.6%.
The reports about the emerging rescue plan come after the annual meeting of the IMF in the US capital last week.
The package is expected to involve a quadrupling - from the current 440bn euros - in the firepower of Europe's main bailout fund, the European Financial Stability Facility (EFSF).
This would be done by putting in place an arrangement that would allow the European Central Bank (ECB) to lend alongside the fund, our editor says.
The EFSF would take on the main risk of lending to governments struggling to borrow from normal commercial sources - governments like Italy.
In this way, the EFSF would make it less dangerous for the ECB to lend.
It is also thought that private investors in Greek debt are likely to have to accept a 50% reduction in what they are owed, our editor says.
After talks with IMF chief Christine Lagarde, Greek Finance Minister Evangelos Venizelos has said that Athens will do "whatever it takes" to reduce its huge deficit, which is currently about 160% of the country's gross domestic product.
Publicly, world leaders have said there is "no plan" for a Greek default, but reports suggest officials are working on a plan to allow Greece to default on some of its debts and remain in the euro.
The third element of the rescue plan envisages a strengthening of big eurozone banks, which are perceived to have too little capital to absorb losses.
