If O'Neill had taken the job, he would have been free to walk away without the FAI reeceiving any compensation.
O'Neill met the Stoke hierarchy last night about taking over at a club sitting 18th in the Premier League.
Keane was tipped as O'Neill's potential successor in the national gig but could now be with him at the Potteries.
McCarthy previously managed Ireland between 1996 and 2002, agonisingly missing out on qualification to the 1998 World Cup and Euro 2000, before leading his troops through to the 2002 World Cup, and then the last-16.
Ireland may have only friendlies scheduled until the Uefa Nations Cup kicks off in September, yet the financial risk of losing their Premier League status means the new manager's focus can not be distracted by extra-curricular activities.
Other loyal members of his coaching staff, including Steve Guppy, Steve Walford, and goalkeeping coach Seamus McDonagh, are also set to follow O'Neill from the Ireland camp into the new adventure.
RTE pundit Dunphy has been critical of O'Neill in the past but this time has taken aim at the association.
The 65-year-old was free to hold talks with the Premier League side as he has not yet signed a new contract with the FAI, despite a verbal agreement to commit to the Ireland job for another two years.
"I can't think of any other Association that would allow their manager to stall in this way", Dunphy told News At One on RTÉ Radio 1. It appears that O'Neill, whilst having agreed a contract with the FAI was still open to offers from others.