In an interview with the Financial Times, Greek Finance Minister Yanis Varoufakis said the leftist-dominated government in Athens would be making proposals for "a menu of debt swaps" that would avoid the need for any of the country's mountain of foreign debt to be written off.
Under an approach he described as "smart debt engineering," Varoufakis proposed the issuing of two new types of bonds.
One would be linked to nominal economic growth to refinance European rescue loans and the other would be "perpetual bonds" that would replace Greek bonds owned by the European Central Bank.
The approach would avoid creditors having to take a hit on the Greek debt, an outcome that is fiercely opposed by several EU countries led by Germany, and would be politically hard to stomach for the likes of Ireland, which was forced to stick to a painful programme of spending cuts as a condition of its own bailout in the aftermath of the 2007 financial crisis.
Varoufakis was to hold talks in Rome with his Italian counterpart Pier Carlo Padoan while Prime Minister Alexis Tsipras will travel from Cyprus to meet with his Italian counterpart Matteo Renzi over lunch.
The debt swaps proposal is likely to get a sympathetic hearing from Renzi, who is well-placed to broker an end to the confrontation as he has the ear of German Chancellor Angela Merkel but is in the camp of those in the EU who want a more flexible, growth-first approach to the bloc's economic policy.
"I believe it is crucial to send a clear message: we want to move the discussion on economic policy from austerity and rigour towards growth and investment," Renzi said on Monday.
"We have to change economic policy at the European level, not just for Greece or any other country."
The stakes involved in the stand-off were underlined on Monday by British finance minister George Osborne, who warned that a potential failure to resolve the crisis was "fast becoming the biggest risk to the global economy."
Despite a restructuring in 2012, Greece is still lumbered with debts of more than €315 billion, upwards of 175 percent of gross domestic product, an EU record. Greece would need to dedicate its entire annual wealth for two years to repay the amount.
An academic and popular blogger, Varoufakis also held talks on Monday with City of London bankers hosted by US giant Merrill Lynch, with a Greek government source saying he wanted to encourage investment and reassure bondholders.
The new Greek administration, which has hired investment bank Lazard to advise it on how to manage its debt, was boosted by comments from US President Barack Obama on Sunday, who warned against "squeezing" Greece.
Tsipras has dismissed the "troika" system monitoring Greece's economy - the International Monetary Fund, European Commission and European Central Bank - as lacking legal status, and blames Germany for driving the tough austerity programmes his hard-left government has pledged to end.
Merkel has ruled out debt relief and on Monday said "tough talks" lay ahead.
A top European Central Bank official piled on further pressure last week, warning that the bank could not keep lending to Greece unless an agreement is found before a February deadline.
But Greece is arguably in a strong negotiating position because of the chaos that could ensue if no solution is found.
The Finnish Finance Minister Alexander Stubb said on Monday that Greece's loan repayment period could be extended, while the governor of the Bank of France ruled out cancelling debt but said some "accommodation" could be found.
Syriza's stunning election success and the formation of a coalition government with the nationalist Independent Greeks has sent shockwaves through Europe.
In its first week in power, the government scrapped the privatisation of Greece's two main ports and the state power company and announced a major increase in the minimum wage.
But Tsipras has tried to calm nerves by saying he did not intend to renege on commitments to the EU and IMF.