BANK of Ireland is understood to have lined up Scottish banker Archie Kane as the next chairman of the bank's board, known as the Court of Governors.
Last night, the bank remained tight-lipped on the issue, refusing to confirm an appointment that has yet to be approved by the Financial Regulator.
A spokesman for the bank also refused to confirm that chairman Pat Molloy was planning to stand down.
However, the Bloomberg newswire reported that Mr Kane had been nominated by Bank of Ireland's board to take the chairman's job, and said he was now going through the Central Bank's process to approve bank directors.
Any new Bank of Ireland chairman will replace Mr Molloy. He was re-elected to the bank's board at the most recent annual general meeting in April this year, but is rumoured to be planning to stand down.
Mr Molloy was CEO of Bank of Ireland from 1991 to 1998 and returned to the bank to take up a position on the board in 2009, and ultimately became chairman.
If Mr Kane does end up taking the Bank of Ireland job, it will mean the boards of all three of the State's remaining bailed-out lenders will have a UK-based chairman.
Mr Kane would benefit from his previous experience on the board of a partially state-owned bank.
He was a director of the UK's biggest lenders, Lloyd's Group, from 2000 until he retired last year.
Mr Kane would become the third UK-based banker responsible for a major state investment in a bank.
AIB chairman David Hodgkinson is a former executive with HSBC.
The new chairman of Permanent TSB, Alan Cooke, is a former managing director of the UK Post Office.
Bank of Ireland remains 15pc state-owned, but it is the only one of the main Irish banks that is not largely in state hands following the banking crisis.
The bank came close to full nationalisation before last year's sale of a 34.9pc stake to a consortium of five US and Canadian investors.
An extraordinary general meeting (EGM) of BoI shareholders is to be held on June 18.
Shareholders are being asked to vote on a request from the Government for a €3.01bn loan to help the State to defray the cost of bailing out Anglo Irish Bank.
(Additional reporting by Joe Brennan at Bloomberg)