Delaney said that the pair had still to sign contracts but that he saw no impediment to O'Neill taking over from Giovanni Trapattoni, who quit in September, and that the former Aston Villa and Celtic boss would be unveiled on Saturday.
"Almost done now. There's nothing I think that will be an impediment in terms of Martin being manager and Roy as his assistant," Delaney told the Newstalk radio station.
O'Neill, once touted in the media for a big club job in England after winning three Scottish league titles and reaching the UEFA Cup final in a successful spell at Celtic, was sacked as manager of struggling Sunderland earlier this year.
He will be charged with picking up an Ireland team that finished in fourth place in the recent World Cup qualification campaign and were outclassed at Euro 2012 when Trapattoni was widely criticised for his negative tactics.
The ex-Northern Ireland international was favourite to take over from Trapattoni after the Italian quit following a poor run of games but Keane's return as his number two is an intriguing move by Delaney and his association.
The former Manchester United midfielder, regarded as one of the country's greatest players, had a major fallout with the FAI over what he saw as amateurish preparations for the World Cup in Japan and South Korea, and despite returning to play two years later, he has remained a vocal critic of the association.
Keane, who also had a stint in charge of Sunderland but saw his coaching ambitions stall during an unsuccessful period at second tier Ipswich Town, slammed Delaney for being pictured drinking with fans during last year's championship.
But it is the seven-times Premier League winner's withering evaluation of then-manager Mick McCarthy and of the FAI in general on the eve of the 2002 World Cup that means he remains one of the most divisive figures in Irish football.
The fiery midfielder threw the national team into chaos when he walked out and the incident dominated the front and back pages of newspapers for days, even being depicted in a musical that compared the dispute to a Shakespearean tragedy.
"Anything that would have been said by Roy or I to each other or about each other is now irrelevant," said Delaney, who added that the imminent appointments would not have been possible without the continued financial support of media mogul Dennis O'Brien.
"He (Martin) asked what the association's view would be in terms of Roy being the assistant and I said absolutely no problem. I met him (Roy) last week and we've discussed the past. It was discussed for about 30 seconds."
"This is a roller coaster that me and most of the Irish people are looking forward to."
(Additional reporting Sam Cage and Phil O'Connor, Editing by Pritha Sarkar)
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