Germany's Chancellor Angela Merkel has vowed to implement a permanent bail-out facility amid speculation over a break up of the 16-nation eurozone.
A joint statement with French President Nicolas Sarkozy said the two would propose replacing the existing fund that expires in 2013.
Meanwhile the head of Germany's central bank said the existing fund could be increased if needed.
And the fund's head has dismissed the risk of a eurozone break-up.
Klaus Regling of the European Financial Stability Facility (EFSF) said it was "inconceivable that the euro fails".
There has been speculation that some countries may be forced to give up the euro in light of the Irish debt crisis.
In their joint statement, the French and German leaders said that they were working "under high pressure on a joint proposal for a crisis mechanism that is to replace the current one beyond 2013".
The EFSF was set up over the summer as a general rescue fund for eurozone governments, in a failed attempt to prevent the Greek debt crisis spreading to other countries.
The two leaders also said they wanted a bail-out of the Irish Republic by the EU and IMF to be finalised as soon as possible.
The negotiators plan to conclude talks on Sunday, according to news agency Agence France Presse, citing an anonymous source in Brussels.
Much of the money for the Irish bail-out will come from the EFSF.
In separate comments, Axel Weber - head of Germany's central bank - said that the EFSF could be increased in size by a further 100bn ($134bn, £85bn) euros if need be.
It comes after the German finance ministry was forced to deny a story in German newspaper die Welt that the 440bn euros fund would be doubled in size.
Moves are also under way to carry out a new and tougher round of stress tests on Europe's biggest banks next year, after a run on the government-guaranteed Irish banks forced Dublin to seek its rescue from the EU and IMF.
Worries about the finances of other eurozone governments - in particular Portugal and increasingly Spain - are putting pressure on the euro and government bonds.
The currency has fallen by more than three cents against the dollar this week because of events in the Irish Republic.
The single currency rallied back slightly in Thursday afternoon trading to $1.3375, but has still lost 3.4 cents or 2.5% of its value against the dollar since the beginning of the week.
The euro has fallen 1.2% since Monday against the pound.
The bond yields of debt-troubled eurozone governments have continued to rise, suggesting that markets are becoming ever less comfortable about lending them money.
The 10-year Irish bond yield rose to 9.08% - above the highs seen prior to the start of the bailout talks. Spanish bonds also fell in value, raising the 10-year yield to 5.2%.
In or out?
Meanwhile, Mr Regling - the EFSF's head - told Germany's Bild newspaper there was "zero chance" that the euro would collapse.
"No country will voluntarily give up the euro - for weaker countries that would be economic suicide, likewise for stronger countries," he said.
Germany's Chancellor, Angela Merkel, also chimed in, saying that she was "more confident than this spring that the European Union will emerge strengthened from the current challenges".
It follows more negative comments she made earlier in the week, when she described the euro's plight as "exceptionally serious".
Questions have been raised about the cost to the EU, and the International Monetary Fund, of bailing out eurozone members - over the summer, Greece was bailed out to the tune of 110bn euros ($147bn; £93bn), while the Irish Republic is currently negotiating what is expected to be an 85bn-euro rescue package.
Many commentators have also pointed out that eurozone countries are unable to devalue their own currency - one of the key methods many governments use to trade their way out of recessions, as a weaker currency makes exports cheaper.
As a result, some have suggested that countries like the Irish Republic and Greece would be better off outside the zone.
Meanwhile, the EU intends to hold a new round of stress tests next year, to check the robustness of Europe's banks.
European officials claim that the new tests will be much more stringent than a previous set of tests carried out over the summer.
"We can expect truly demanding tests over the course of 2011," said Jonathan Faull, head of the internal market unit of the European Commission.
The European Central Bank is said to want to include an additional test of whether banks have enough cash in reserve in case they suffer the kind of deposit flight that afflicted those from Ireland.
The results of the first stress tests were published in July in a bid to reassure markets during an earlier chapter of the sovereign debt crisis.
Of the 91 major European banks scrutinised, only seven - in Greece and Spain - failed.
All of the major Irish banks passed. However, now the Irish government is set to almost completely nationalise Allied Irish Banks and Bank of Ireland.