The Baggies are on the hunt for a new boss after Sam Allardyce opted to leave the club at the end of the season.
Wilder had been the long-standing favourite with the bookmakers to land the job – with his odds as short as 1/8 on at one stage.
But he is now the second favourite with those odds having drifted to 7/4.
Current Lincoln manager Michael Appleton is now the frontrunner with the bookies. The former Albion midfielder is priced at evens for the role.
And it is understood the Baggies are willing to pay compensation if they feel the manager to take them forward is currently in work.
According to reports, Albion would have to pay £700,000 to Lincoln if they want to appoint Appleton as boss.
Wilder’s odds have drifted in recent days after reports emerged claiming that the Baggies have called off their pursuit of the former Sheffield United boss.
But the Express & Star understands that is not the case with the 53-year-old still under consideration for the role.
It is also understood Wilder is keen on taking charge at The Hawthorns.
Allardyce confirmed he would leave Albion almost three weeks ago.
And in the time that’s passed, some fans have grown concerned the club hasn’t yet made an appointment.
Albion, though, haven’t wanted to rush things – with the Express & Star understanding the final round of interviews took place over the weekend.