The German boss met technical director Luke Dowling last week, but has since fallen down the pecking order.
Albion’s shortlist has evolved in the last seven days due to a number of new candidates becoming available in the close-season.
Labbadia is not out of the running, and reports Albion have baulked at his wage demands are believed to be wide of the mark, but the Baggies are currently speaking to other contenders.
Chris Wilder has emerged as a potential shock appointment due to his frustrations at the ongoing legal battle between Sheffield United’s joint-owners Kevin McCabe and Prince Abdullah of Saudi Arabia.
It’s believed Wilder wants reassurances over his transfer budget from United’s decision-makers after winning two promotions in three years for his boyhood club.
He is concerned in-fighting is damaging preparations for United’s first season in the Premier League for 12 years.
However, Albion’s chance of appointing him remains a long shot for now with Wilder most likely to stay at Bramall Lane. Middlesbrough are also keeping an eye on the situation.
The Baggies, meanwhile, are speaking to two other unnamed candidates who have recently emerged.
Two weeks ago, Dowling revealed he had a four-man shortlist to work through, but the figures in contention have subsequently changed.
Chris Hughton, who was previously in contention, would have required to take a pay cut to join the Baggies, while Danny Cowley’s methods were not in-keeping with Albion’s model.
It is now three weeks since the Baggies lost to rivals Villa in the play-offs, and supporters are beginning to grow frustrated their club remain managerless.
However, Albion’s hierarchy are not concerned by how long the search is taking.
They do not want to rush into the wrong decision and believe this time of year, when players are on holiday and not training, is the perfect time to explore all viable options.
Albion’s squad is also likely to look vastly different come the start of the season.
A big overhaul in players is expected once the new head coach is appointed and the transfer window kicks into gear with several high-profile and older players making way for a new crop.