The Baggies are on the lookout for a permanent successor to Alan Pardew and believe that Allardyce could be the man to lead them back to the Premier League next season, after doing the same with Bolton and West Ham in the past.
Albion are still alive in the Premier League following an impressive run under caretaker boss Darren Moore, but it looks to have come too late to save them from the drop, and the Baggies board are planning for next season.
Some believe Moore has shown enough to get the job, but that looks unlikely as reports claim Albion have already made contact with Everton officials over a potential move for Allardyce.
Big Sam has guided Everton away from danger since taking charge, picking up more points than any club outside of the top five, but his style of play has not gone down well with the Toffees faithful, with a large number wanting him out.
The Everton board may not agree though and there is every chance Allardyce will remain at Goodison Park for at least one more season.