* Irish government selling 25 percent of state-owned bank
* Sale could raise 3 bln euros, price under 5 euro per share
* AIB CEO not worried about potential impact of UK election (Adds CEO quotes, details, link to Reuters Breakingviews column)
By Padraic Halpin
DUBLIN, May 31 (Reuters) - Allied Irish Banks is attracting very significant investor interest as Ireland begins returning the bank it rescued almost a decade ago to private ownership, its chief executive said on Wednesday.
One of Ireland's two dominant banks, AIB has been profitable for each of the last three years and is the largest provider of mortgages in the fast-recovering Irish economy.
Against this backdrop the Irish government launched its long-awaited initial public offering of AIB on Tuesday, offering a 25 percent stake in what is set to be one of Europe's largest bank listings since the 2008 financial crisis.
Dublin, which rescued the bank in a 21 billion-euro taxpayer bailout that began almost a decade ago, has been considering partly cashing out of its 99.9 percent stake for more than a year and the bank has been meeting investors since then.
"The combination of a strong Irish economy with a growing European economy as a backdrop and a strong franchise here means that there is very significant investor appetite," AIB chief executive Bernard Byrne told national broadcaster RTE.
While a chronic lack of housing could hold lending back, Byrne said investors see AIB's forecast that the overall Irish market will almost double to 10 billion euros in the medium term as an attractive selling point.
Byrne said he anticipated that the stake would be sold to a wide variety of institutions who would take a long term view.
Irish Finance Minister Noonan declined to say how much Dublin expected to raise, adding this could "give investors traction to push the value down" ahead of the publication of a price range in mid-June
Analysts say it could raise around 3 billion euros, based on the bank's book value of 11.3 billion euros at the end of last year and the fact that it has continued to generate capital and resumed dividend payments since.
Based on the number of shares outstanding, and allowing for an improvement in the bank's finances in 2017, the price is likely to come in below 5 euro per share, IFR, a Thomson Reuters publication, estimated.
Noonan said the price could be "driven up a little" if Britain's ruling Conservative party wins a strong majority in a June 8 election. But a poll published shortly after his comments showed they could in fact lose their majority.