Ireland's central bank has written to the CEOs of Bank of Ireland , Irish Life & Permanent and EBS Building Society warning them that they face possible investigation over their roles in the run-up to the country's banking crisis, sources said on Friday.

Ireland's government, which controls all local lenders bar Bank of Ireland, said last year it wanted to clear the sector of board members appointed before a lending and funding crisis hit the industry in September 2008.

This pushed the country into an eventual EU-IMF bailout and has forced taxpayers to shell out tens of billions of euros in capital to avoid the banking sector's collapse.

Bank of Ireland's Richie Boucher, Irish Life & Permanent's Kevin Murphy and EBS' Fergus Murphy were executive directors before the crisis hit.

Ireland's central bank introduced a new regime for scrutinising bank boards on December 1 giving it the power to veto future senior appointments or fire existing senior bank staff.

The central bank wrote to the three bank CEOs in December seeking their response to the possibility of an investigation into their pre-crisis roles, sources familiar with the situation told Reuters.

The central bank will appoint an independent arbitrator, likely to be a retired judge or a senior lawyer, in the coming weeks who will decide whether the bankers should face an investigation to determine whether they should remain in their jobs.

If an investigation is launched, a separate independent arbitrator would lead the probe, which would likely take some months to conclude.

The central bank said it would not comment on individual cases.

As previously announced, the central bank is reviewing the position of executive and non-executive directors of covered institutions that received state support and who are remaining in director posts after January 1, a spokesman said in a statement.

This process provides opportunities for individuals to make representations and will involve independent decision makers appointed by the central bank.

EBS and Bank of Ireland declined to comment.

A spokesman for bancassurer Irish Life & Permanent confirmed that Kevin Murphy had received a letter but said he had resigned as a director of its bank last month in preparation for the separation of the life business from the bank by an end of March deadline.

We can confirm that we received a letter but it is not applicable to us, the spokesman said.

Boucher has been a member of Bank of Ireland's executive board since 2006 and was appointed chief executive in February 2009 despite the objections of some shareholders who opposed the promotion of a company insider to the top job.

Boucher's success last year in wooing North American investors to buy a 35 percent stake in Bank of Ireland, capping the government's stake at 15 percent, bolstered his position.

The chief executive of one of the investors, Canada's Fairfax Financial Holdings , told Reuters that Boucher had impressed him.

Fergus Murphy joined EBS as chief executive in January 2008 from ACC Bank, a unit of Dutch group Rabobank. EBS was merged with the much larger Allied Irish Banks (AIB) last year and Murphy is currently in charge of restructuring the merged group.

(Reporting by Carmel Crimmins. Editing by Jane Merriman)