Bookies are already taking bets on the matter, with a couple of familiar faces heading the longlist.
Mick McCarthy 5/1
The last man to lead Ireland to a World Cup, McCarthy ended his six-and-a-half-year tenure in November 2002, not long after the Saipan incident.
History has looked well on the McCarthy years and he’s been regularly in work since then, with Sunderland, Wolves and Ipswich.
However, with Tractor Boys’ fans growing ever restless with McCarthy and the subject of his contract, which expires this summer, yet to be broached by the club, his long-term future may not be at Portman Road.
Ireland have only friendlies with Turkey and France scheduled before the inaugural UEFA Nations League kicks-off in September.
Roy Keane 11/2
O’Neill’s assistant manager with Ireland, Keane has openly spoke about a return to a top job in the future.
It’s been seven years since he was dismissed by Ipswich, so managing the Boys in Green could prove a likely path back to a lead role.
However, Stoke reportedly want a quick hire so O’Neill transplanting his backroom team, including Keane, en bloc to the Britannia would make sense for them.
Would he consider a job-share after quitting a similar role at Aston Villa in November 2014?
Neil Lennon 10/1
The former Northern Ireland international has had plenty of success in Scotland, winning three titles with Celtic and leading his current club Hibernian from the Championship to fourth in the Premiership, but had a less enjoyable time at Bolton.
He is a regular pundit with TV3.
Stephen Kenny 12/1
The Dundalk manager’s attacking side was hailed as a counterpoint to O’Neill’s safety-first approach by pundits as the Lilywhites put in an impressive Europa League performance in 2016.
With a three-in-a-row of league titles and plenty of managerial awards, Kenny has more than proven himself in the domestic league.
Paul Clement 12/1
Available since being sacked by Swansea last month, Clement is trying to establish himself as a number one after gaining some impressive experience as an assistant to Carlo Ancelotti at Chelsea, PSG, Real Madrid and Bayern Munich.
He may still find himself in demand in England, however.
Michael O’Neill 14/1
The Northern Ireland manager has been in talks with Scotland, who have reportedly offered to make him the highest-paid boss in the history of the national side.
He previously proved himself in the League of Ireland and Europa League with Shamrock Rovers.
Ryan Giggs 14/1
Giggs seems to have been linked with ever job under the sun since his four games in temporary change of Manchester United. A more likely frontrunner for the vacant Wales job.
Odds via Paddy Power.