The Bank of Ireland has declined to comment on reports that its chief executive, Brian Goggin, is preparing to quit his job in a few months.

But industry sources in Dublin say Mr Goggin, who earned a record €4m in 2007, is likely to be the first of several top bankers to depart voluntarily after the injection of Irish taxpayers’ money into the banks in March.

It is believed that the process would have begun already, had it not been for the forced resignations of Anglo-Irish chairman Sean FitzPatrick and chief executive David Drumm over the concealment of more than €80m in loans from the bank to Mr FitzPatrick.

Other top executives, who officially will be leaving of their own accord, did not want to be associated with the Anglo departures.

At the weekend, Irish Financial Regulator Patrick Neary announced his retirement after an investigation failed to find out why the Finance Minister was not informed as soon as the existence of the loans was discovered. Anglo’s finance director, Willie McCarter, also stepped down.

Mr Lenihan is understood to feel that all the bosses of the six guaranteed banks should leave after the injection of €7bn of public funds to boost their depleted capital, along with most of their directors.

In an interview last week, he said it was not generally appreciated “how far the banks had departed from their moorings”.

The chief executive most likely to hold on, if he wishes to, is believed to be AIB boss Eugene Sheehy. But Mr Sheehy abandoned his pledge not to take any Irish government funding, which may weaken his position. An AIB spokeswoman said: “Eugene Sheehy has the full support of the AIB board and there is no question of his resignation.”

One potential problem for Mr Lenihan is that the top bankers who have not been accused of any actual wrongdoing may be entitled to six-figure severance terms, of the kind which caused the furore in Aer Lingus. Any such payments are likely to produce a similar uproar among taxpayers, small shareholders and opposition politicians.

The taxpayer’s potential exposure to the banks appears to be growing, amid fears that the banks will not be able to raise capital on the stock markets, and a High Court ruling which could accelerate their losses.