AIB intends to promote its retail and business unit head Bernard Byrne to become the bank's new chief executive.
According to the Bloomberg news service, the bank is seeking permission from regulators for the move.
The news agency cited a person with knowledge of the matter.
Mr Byrne’s name has been given to the European Central Bank’s banking supervision unit for confirmation.
The timing of approval is not yet clear, said the person, who asked not to be identified as the process is not yet complete, Bloomberg added.
It said that officials from AIB, the Central Bank and and the Department of Finance in Dublin and the ECB in Frankfurt declined to comment.
AIB has been searching for a new CEO since January, when David Duffy said he was leaving to join National Australia Bank's Clydesdale Bank.
The new CEO is set to lead the bank back to private ownership, with Finance Minister Michael Noonan saying in February that the Government may start selling its stake as soon as October.
The bank identified Byrne, 46, as the leading internal candidate two months ago, a person familiar with the matter said.
A chartered accountant, Byrne joined AIB in 2010 as chief financial officer, after working with the ESB. He joined AIB’s board in July 2011.