O'Neill has been out of work since being sacked by Sunderland in late March, but the former Northern Ireland international is now poised to succeed Giovanni Trapattoni.
Veteran Italian coach Trapattoni left his position in September after Ireland's World Cup hopes had ended and Noel King took charge for the final two qualifiers against Germany and Kazakhstan.
Former Celtic boss O'Neill was immediately put forward as a leading candidate to replace Trapattoni, along with ex-boss Mick McCarthy and Keane.
It is understood that O'Neill wanted time to think about the possibility of becoming an international coach, but he held talks with Football Association of Ireland officials on Friday.
The exact terms of a contract have yet to be discussed, but O'Neill expressed his interest in taking the job and an announcement could be made in the next few days.
The FAI is keen to appoint O'Neill before the home friendly with Latvia on 15th November and the players meet up for a training camp on Sunday 10th November.
O'Neill is also hoping to name former Ireland captain Keane as his No.2, with his long-time assistant John Robertson currently recovering from a heart attack.
Keane has held talks with the FAI about becoming O'Neill's assistant and he has been out of management since being sacked by Ipswich Town in January 2011.
He was infamously sent home from the 2002 World Cup in the Far East by then-coach McCarthy following his criticism of the squad's training facilities.
The ex-Manchester United captain also has a frosty relationship with John Delaney and has publically criticised the FAI chief executive in the past.