The Republic have been without a permanent manager since the September departure of Giovanni Trapattoni, after which the experienced O'Neill quickly became the leading candidate.
Former captain Keane - who infamously walked out on Ireland during the 2002 World Cup - has since emerged as the man O'Neill wants to serve as his assistant and an announcement could come later on Tuesday.
"We can confirm that the management appointment process with Martin O'Neill & Roy Keane is at an advanced stage.Updates from @FAIreland today," the governing body said on its official Twitter account.
O'Neill was identified as the FAI's primary choice within days of Trapattoni's departure following the defeats by Sweden and Austria which effectively ended Ireland's hopes of making it to next summer's World Cup finals in Brazil.
However, the FAI has allowed the 61-year-old, who has been out of the game since being shown the door by Sunderland in March, to take his time over his decision.
In the meantime, former Republic international Ray Houghton and high performance director Ruud Dokter were charged with the task of assessing alternative candidates.
But all along, the power brokers have been hoping for a positive response from the Northern Irishman, and things have moved on apace since he gave the first indications that he was ready to commit himself to Ireland.
While O'Neill's appointment may have come as no surprise in the circumstances, the identity of his number two has raised eyebrows.
Keane, of course, enjoyed a distinguished international career with the Republic, but fell out spectacularly with then manager Mick McCarthy as they completed their preparations for the 2002 World Cup finals in the Far East and returned home without kicking a ball in anger.
Time appears to have healed any lingering wounds and there is little doubt that a link-up between two men who as individuals enjoy popular support will capture the imagination of fans who became disillusioned with Trapattoni's conservatism once results began to elude him.
The 74-year-old spent five and a half years at the helm with businessman Denis O'Brien providing a significant proportion of the funding - he will continue his financial support - and that investment initially paid dividends.
Trapattoni guided the nation to a play-off clash with France and only William Gallas' goal, which came courtesy of Thierry Henry's infamous handball on a controversial night at the Stade de France, denied them a trip to the 2010 World Cup finals in South Africa.
The Italian went one better in the following campaign when he safely negotiated a path through the play-offs to take his team to Euro 2012 in Poland and Ukraine.
But as fans travelled in their thousands in hope of a repeat of previous heroics on the big stage, Ireland were overwhelmed by Croatia, Spain and Italy and returned home without a point to their name.
Undaunted, Trapattoni embarked upon the qualification process for Brazil with an unconvincing win in Kazakhstan, but a 6-1 demolition by Germany at the Aviva Stadium left him fighting for his job and although he survived another 11 months, the writing was on the wall.
O'Neill and Keane, who also had a spell in charge of the Black Cats, will launch their reign with a friendly against Latvia in Dublin on November 15, when the FAI will hope the public vote with their feet by turning out in force, before heading for Poland four days later.
The serious business will begin in September next year when the Republic set out on the road to Euro 2016 hoping they can once again compete for a place at the finals of a major tournament, the mission assigned to their new managerial duo.
- Sports & Recreation
- Giovanni Trapattoni
- Roy Keane