The Black Country outfit had interviewed Alan Curbishley, Neil Warnock and Steve Bruce but were left having to widen their search after all three turned their backs on the job.
Reading’s Brian McDermott is also believed to also be on the Molineux club’s shortlist and is considered a more likely option than Poyet because of his greater experience in the second flight.
Poyet has previously said he would remain loyal to the Albion unless faced with an offer he considered too good to turn down.
However, with a relative inexperience in management and a CV which currently boasts a single promotion from League One, the popular boss is unlikely to be in the running for more high profile vacancies in the near future.
Online bookies SkyBet currently have Poyet as joint second favourite at 5/2 with McDermott at 9/4.