The Department of Finance is to place advertisements in the national newspapers seeking people who are interested in being appointed or nominated to the boards of the banks.
The department said the adverts would give anyone interested in and qualified to act as a director the chance to advise Minister for Finance Michael Noonan of their interest.
It said the move would make the appointment process more open and transparent and was part of commitments given in the Programme for Government to restructure bank boards.
People who are interested must apply by Thursday 12 May.
The advert says that to qualify for appointment, a person 'must not have any conflicts of interest likely to interfere with his/her ability to play a full part on the board'.
Any person expressing an interest must also have 'considerable expertise' in financial services and experience at a senior level in one or more of ten listed areas.