The Central Bank has warned the chief executives of Bank of Ireland, Irish Life and Permanent and EBS that they may be investigated as part of the regulator’s new fitness and probity rules.

The three bankers are the only remaining executives on the boards of the State-backed banks who have held their jobs since before the beginning of the financial crisis in 2008.

The regulator has stepped up plans to scrutinise long-serving bank executives, issuing letters last month to Bank of Ireland chief executive Richie Boucher, Irish Life and Permanent chief executive Kevin Murphy, and Fergus Murphy, chief executive of EBS.

The Central Bank warned them that there may be grounds to investigate their roles at their institutions prior to the banking crisis under the fitness and probity rules.

Responses were sought from the bankers on the possibility that an investigator could be appointed to examine their pre-crisis roles.

The tests came into effect last month as part of sweeping regulatory reforms introduced in the wake of the €63 billion banking crisis.

The Central Bank warned last year that any pre-crisis bank directors who wished to remain on after the start of this year would face the tests.

The Central Bank had no comment. Mr Boucher and Fergus Murphy also declined to comment.

Irish Life and Permanent confirmed that Kevin Murphy received the letter but said he resigned as a director of its bank last month and that this removed him from the regulator's tests.

"In preparation for the separation of the life business and the bank by the end of March 2012, Kevin Murphy stepped down as a director of the bank and therefore this process doesn't apply to him," said a spokesman for the group.

Mr Murphy resigned as a director of Irish Life and Permanent Plc, which trades as Permanent TSB bank, but he remains a director of the group's overall holding company, Irish Life and Permanent Group Holdings plc, and Irish Life.

The group is being split up with the division of the life and pensions business, Irish Life, and Permanent TSB with a view to the life business eventually being sold off.

The Central Bank will appoint an independent arbitrator, mostly likely a senior lawyer, in the coming weeks who will decide whether the bankers should face an investigation to determine whether they are fit or proper to remain on as directors in light of their pre-crisis roles.

The bankers will be able to make submissions in their defence.

The investigations will determine whether their actions prior to the 2008 bank guarantee, which the Government believed would save the banking sector, contributed to the subsequent cost of the State bailouts of their institutions.

The State has injected €2.7 billion into Irish Life and Permanent, effectively nationalising the company.

Some €4.2 billion of public money has been injected into Bank of Ireland but it has avoided State control after the Government sold a 35 per cent stake to private investors in July 2011. Mr Boucher has been chief executive since February 2009.

Nationalised EBS has received €2.4 billion from the State and been merged into AIB, which is 99.8 per cent State owned.

Kevin Murphy is the longest serving of the remaining pre-crisis directors. He has sat on the Life and Permanent board since 1999.

Mr Boucher was appointed to the board of Bank of Ireland in 2006 and played a pivotal role in the growth of the bank's lending to the property sector from 2004.

Fergus Murphy's appointment as chief executive of EBS in January 2008, just nine months before the guarantee, makes him eligible for possible investigation under the fitness and probity tests.

Bank of Ireland's announcement two days before Christmas that its two remaining pre-guarantee non-executive directors would be stepping down cleared out the remaining non-executive directors at the guaranteed banks.