With the few bookmakers still accepting bets, O'Neill is best priced at just 1/9 to be appointed.
According to the Irish Independent, the recruitment team of Ray Houghton and Ruud Dokter will not present their report to the association's hierarchy until Monday but a number of bets have already been put on O'Neill getting the job.
The paper adds that O'Neill has been in contact with the FAI through intermediaries this week.
The other main contender for the job has been Ipswich boss Mick McCarthy but their managing director Ian Milne confirmed: "We've had no approach – the owner, us at the club, or Mick."
O'Neill has been out of football since losing his job at Sunderland at the end of March with the club fighting for Premier League survival.
He had been drafted in by the Black Cats in December 2011 in a move craved for so long by many supporters, and his initial impact was little short of spectacular.
However, having dragged Sunderland clear of the basement battle in which they were engaged on his arrival, he struggled to take them to the next level despite being allowed to invest around £22million in Scotland striker Steven Fletcher and England winger Adam Johnson during his only summer transfer window.
By the time he was shown the door after a dour 1-1 home draw with 10-man Norwich, O'Neill's legendary enthusiasm appeared to have deserted him.
However, the Ulsterman is understood to be keen to return to the game, and the challenge of international football is one which appeals.
It was perhaps significant that he was unable, despite several attempts, to persuade long-time ally John Robertson to join him on Wearside, and it would be no surprise if he wanted the Scot to do just that in Ireland.
However, Robertson is currently recovering after suffering a suspected heat attack in August and that could preclude his involvement.
- Sports & Recreation