Bernard Byrne, AIB's director of retail and business banking, is leading the race to replace David Duffy as the bank's chief executive, sources inside the bank say.
The bank has a shortlist and a second round of interviews for the post is set to be held within the next two weeks, Finance Minister Michael Noonan told the Sunday Independent.
Mr Noonan said the list includes current AIB employees as well as external candidates.
"They were organising two rounds of interviews. The first was kind of informal, having a chat, and then they were having formal interviews.
"I'd say they are this week or next week, the next couple of weeks," Mr Noonan said.
Other internal candidates in the running for the post are thought to include chief financial officer Mark Bourke and director of corporate and institutional banking Fergus Murphy.
Last week, AIB chairman Richard Pym said the bank needed to "get a move on" as it hunts for a replacement for Mr Duffy.
Mr Duffy is leaving in the summer to take over at Clydesdale Bank in Scotland.
The new chief executive's salary will be capped at €500,000.
Mr Pym said he didn't think the cap would hinder the bank's efforts to find a good chief executive.
AIB is currently trying to rearrange its complicated capital structure before a return to private ownership.
At an event in Dublin earlier this week, Mr Noonan said the earliest possible date for beginning to sell the State's near 100pc stake in the bank is October of this year.
He said the Government would explore floating 25pc of the bank on the London Stock Exchange, and strongly emphasised that the timing of any sale won't be influenced by the next election.
Mr Pym said AIB will be ready for a sale whenever the Government is.
Ciaran Murray, the low-profile chief executive of pharmaceutical researcher Icon, has become the highest-paid Irish chief executive of a listed company.
Last year Mr Murray raked in €11.7m, toppling Aryzta boss Owen Killian, who earned €5.8m in the year ending July 31st last.
Mr Murray earned almost three times more than CRH boss Albert Manifold, though Mr Manifold's company is worth five times as much as Icon.
Icon told the Sunday Independent that its executive remuneration reflects the performance of the company and is benchmarked against its global peers.
Mr Murray's total compensation soared upward from €5.5m in 2013.
The 2014 package included a salary of €1.1m, a bonus of €5.2m, and share-based compensation of €5.2m.
Mr Murray joined Icon in 2005 as chief financial officer and became chief executive in 2011.
Reports filed to the US Securities and Exchange Commission show that Mr Murray has earned around €27m since the year he became chief executive.
At the end of last December he owned 15,149 Icon shares, which currently trade at over $67 a pop on the Nasdaq.
In 2005, he earned around €70,000 having joined the company that October.
In 2012, his €8.9m package was five times what he got in 2011.
Icon had net income of €173m in 2014.
Mr Murray said the company's "excellence in execution, along with our market leading innovative solutions, enabled our customers to enhance the productivity of their development programmes and further consolidated our position as a leader".
Previously he has worked for PricewaterhouseCoopers and software company Novell.
Icon's market capitalisation is $4.4bn. This time last year its shares were trading below $50, meaning they've jumped 34pc in the last year.
The Leopardstown-headquartered company helps drug companies carry out trials and also provides strategic advice.
Sunday Indo Business