Potters chairman Peter Coates and his board made the Derryman their preferred target to replace the sacked Mark Hughes and negotiations in the midlands are due to continue today.
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.
Derby County boss Gary Rowett was originally the leading contender to succeed Hughes, but he signed a new three-and-a-half-year deal with the Championship club on Tuesday.
O'Neill has reportedly always been held in high regard by the bet365 stadium chiefs.
Anti-racism protests hit S. African H&M stores
Video footage showed activists trashing displays, kicking over and pulling down clothes rails as well as pushing over mannequins. This is not the first time the retail giant has come under fire in South Africa.
Former Irish worldwide Kevin Kilbane gave his opinion about what may have a bearing on O'Neill's decision to move on.
O'Neill has still not decided whether to accept their offer as he and his assistant Roy Keane are excited by the challenge of building a new, younger Ireland squad during their European Nations Cup campaign, which starts later this year. That means that Stoke do not have to make a formal approach, and O'Neill is keen on a return to club management.
Should Keane not leave then Steve Walford, Steve Guppy and Seamus McDonagh are in contention for roles. It appears that O'Neill, whilst having agreed a contract with the FAI was still open to offers from others.
The Irish manager was then stung by criticism in the aftermath of the crushing World Cup play-off defeat to Denmark at Lansdowne Road only a month later.