(Adds detail, background, advisers)
By Padraic Halpin and Dasha Afanasieva
DUBLIN/LONDON, June 12 (Reuters) - Allied Irish Banks(AIB) plans to raise up to 3.3 billion euros ($3.7 billion) when it sells a 25 percent stake on the Dublin and London stock markets in the biggest test yet of investor appetite for Irish banks.
The initial public offering (IPO) is set to be one of Europe's largest bank listings since the 2008 financial crisis and the proceeds could extend to 3.8 billion euros if the over-allotment option is exercised fully.
With a price range between 3.90 euros and 4.90 euros, the deal is targeting a similar valuation to that of Bank of Ireland , the state's largest bank by assets.
A source close to the deal said the range was based on a price to book value multiple of between 0.82 and 1.03. Bank of Ireland trades at a multiple of 0.9.
The Finance Ministry said the long-awaited stake sale remains on track despite the Conservative party losing its majority in Thursday's UK election.
Finance Minister Michael Noonan had previously said the price could be driven up if the party, which still won the most seats, secured a convincing majority.
"Market conditions remain favourable and I am encouraged by the strong level of interest shown by investors in the offering to date," Noonan said in a statement.
Dublin rescued the bank in a 21 billion euro taxpayer bailout that began in early 2009 and has been considering cashing out some of its 99.9 percent stake since last year.
One of Ireland's two dominant banks alongside Bank of Ireland, AIB returned to profit three years ago and has since cut its huge stock of impaired loans by more than two thirds become the first domestically owned lender to restart dividends since the financial crisis.
AIB will list its shares on the Irish and London stock exchanges and seek admission to the main markets of each. The government said the sale is expected to be one of the largest IPOs on the UK's main market in 20 years.
AIB is less exposed to Britain's departure from the European Union than bigger rival Bank of Ireland, having made only 14 percent of last year's pre-provision operating profit in the UK.
However, the IPO prospectus said that Brexit could result in an increase in the level of non-performing loans held by banks across Ireland, including AIB, while demand for new loans could decline.
Ireland's substantial stock of non-performing loans, mostly extended for house purchases just before the bursting of Ireland's property bubble in 2008, amounts to 17.5 percent of total lending.
At the end of 2016 AIB's 14.2 billion euros of non-performing loans accounted for 22 percent of its gross loan book. That compares with 9.6 percent at Bank of Ireland.
Bank of America Merrill Lynch, Davy and Deutsche Bank are global coordinators for the AIB offering. ($1 = 0.8929 euros) (Additional reporting by Conor Humphries; Editing by Greg Mahlich and David Goodman)