The former Hibs and Newcastle winger was offered the job in 2016 before Brendan Rodgers was appointed but turned it down to focus on his then job of managing the Northern Ireland national team.
Reports today claim O’Neill remains on the club's radar, with Celtic s Head of Football Operations Nick Hammond having tried to lure the 51-year-old to West Brom in the past.
O’Neill took the reins at Stoke in November 2019, succeeding Nathan Jones and helping take the Potters out of the Championship relegation zone, while this season he has led the side to the top half of the table.
90min reports that O’Neill is still highly regarded by the Hoops hierarchy, and he could be an option going forward.
Meanwhile, David Webb has thrown his hat into the ring for the sporting director role at Celtic. Speaking to The Herald he said: “Given their historical success and how they want to build from their academy and build a long-term strategy for the club and still maintain success by winning leagues and cups, and Europe, that would definitely appeal to me.
"You could have someone like myself whose skillset could affect a number of positive areas like recruitment, vision. It's something that is appealing.”
But Webb, who spent time as Technical Director at Huddersfield Town, also believes former colleague Eddie Howe would be a good shout for the managerial vacancy.
Webb worked closely with the 43-year-old at Bournemouth during a spell as recruitment guru, and believes the Celtic job would be an ideal fit – but expects Howe to have plenty of offers.
He added: “When he was at Bournemouth he was linked with loads of roles, clubs considered higher than Bournemouth, but he wasn't quick to jump.
“It’s always about the project and not necessarily the club or size of the club.
"He will take his time on the right project so if he feels Celtic are that club and can fit in the values that he has, potentially, yes [he would be keen].”