The Baggies are expected to ask the Irish Football Association for permission to speak to O'Neill in the coming days.
Technical director Luke Dowling is beginning the interview process this week, and is planning to speak to his four main candidates over the next fortnight.
O’Neill is one of the names on Albion’s radar, having impressed over the past eight years with the Green and White Army.
Former Brighton boss Chris Hughton, who has been replaced by ex-Albion defender Graham Potter, is also in contention while Lincoln City’s Danny Cowley is another manager on the shortlist.
O’Neill took Northern Ireland to their first major tournament in 30 years when he guided the country to Euro 2016.
His team had three Albion players in it at the time – Chris Brunt, Jonny Evans, and Gareth McAuley.
He was in line for the Scotland job last year but turned down an approach from the Scottish FA to remain at Northern Ireland.
He was keen on the Albion job in November 2017 when Tony Pulis was sacked, but the Baggies appointed Alan Pardew instead.
O'Neill was also sounded out last summer before the Baggies narrowed their search down to Dean Smith and Darren Moore, eventually promotion Moore from caretaker boss to the permanent role.
O’Neill has limited experience in club football, and has never managed in England, having been in charge of Brechin City and Shamrock Rovers before Northern Ireland.
So his appointment would be a bold one after so long in international football.
But the 49-year-old has earned a reputation for getting the most out of his players while in charge of Northern Ireland, who also nearly qualified for last summer’s World Cup in Russia.
Albion sacked Moore in March and caretaker boss Jimmy Shan saw out the rest of the season in charge.
The Baggies are facing a busy summer with a number of high-profile players expected to leave and a raft of new signings needed to fill up a squad that has already seen six loanees return to their parent clubs.