Albion moved swiftly for the 56-year-old after parting company with head coach Alan Irvine late on Monday evening.
A formal approach has been made but understands Pulis, who has been out of management since leaving Crystal Palace before the start of the season, wants full control of transfer activity at the struggling Premier League club.
Pulis has been out of work since his surprise departure from Selhurst Park in August, just two days before the first match of the new season.
Following his arrival in November 2013 with Palace struggling in the league, Pulis kept the club in the top flight and won the??Premier League Manager of the Year award for his efforts.
Should Pulis be appointed by West Brom, he will be the sixth full-time appointment at the club since 2009.