IRELAND will be offered a "safety net" of funding to help it return to the international markets under a plan being examined by the International Monetary Fund.
The IMF might provide extra money as a "backstop" to help reassure international investors about a country such as Ireland returning to the markets.
Such a measure would help smooth the way for a country with a troubled financial history – like Ireland – to borrow on the international markets again.
Finance Minister Michael Noonan, who was also in Davos, said: "We don't want to go back into the market and fall back out of it again."
Under the plan being considered by the IMF, a "safety net" of funding would be available to stop this scenario from happening.
Mr Noonan also said Ms Lagarde will be visiting Dublin in March, her first visit since the Government came to power two years ago. And a delegation from the troika of the International Monetary Fund, the European Commission and the European Central Bank are due in Dublin next week for another progress review.
The troika are due to present a paper on potential arrangements for Ireland to transition out of the bailout.
"We expect to exit our (bailout) programme in 2013," Mr Kenny told a panel discussion at the meeting.
But he said that Ireland could not do it without commitments given by other countries in Europe.
Mr Kenny and Ms Lagarde also discussed the promissory note issue, as the country looks for a way to ease the burden of massive costs linked to Anglo Irish Bank.
It came as the head of the organisation representing global financial institutions said it is "crucial" for Ireland to get a deal on the promissory note issue within the next 60 days.
Charles Dallara, managing director of the Institute of International Finance, said that in the "near term" it was the most important issue for Ireland's return to the markets.
Earlier, the Taoiseach insisted that Ireland is not a haven for "unorthodox tax practices" and said the country's 12.5pc corporate tax rate is transparent.
Mr Kenny was responding to questions about plans among big countries to crack down on tax avoidance.
Mr Kenny appeared uneasy at times as the debate turned to corporate taxes, claiming the Irish system was "very clear, very transparent" and would not be changed.
Mr Kenny also ruled out any referendum in Ireland on new EU treaties until after next year's European elections, but declined to rule out a referendum at a later stage to change treaties along the lines that Britain's David Cameron wants.
Mr Kenny was speaking after a private meeting with Mr Cameron to discuss the British prime minister's vow of a referendum on EU membership.
In an earlier discussion on European issues with the Italian, Dutch and Danish prime ministers, Mr Kenny repeatedly called on Europe to reach agreement on a deal on bank debt. Earlier, Mr Cameron told the same audience he was using his influence in the G8 group of industrialised nations to clamp down on tax avoidance.