Former Wolves boss Mick McCarthy could be invited back for a second spell as Republic of Ireland manager after the departure of Giovanni Trapattoni by mutual consent.
John Delaney, the Chief Executive of the Football Association of Ireland mentioned McCarthy in a radio interview.
"Mick has done a very good job for Ireland and in England as well. We have to look at who can get the best out of the players available to us."
McCarthy managed the Republic from 1996 to 2002, bowing out after a poor start to the Euro 2004 qualifying campaign.
Former Sunderland boss O'Neill has been at the top of the bookmakers' list and remains a firm favourite.
Delaney also insisted that they would not rush their decision:
""We will meet and will determine a process. We do have time. The European qualifiers don't start until next September. We will take stock of the last couple of days and then discuss the process."