The 33-year-old Stoke striker will reportedly be the Welshman's main target.
Indeed, the Welshman will be given a January transfer kitty and full control over recruitment strategy, the report states.
Those responsibilities will come with West Brom's highest ever manager salary, along with a steady survival bonus.
Crouch, 33, is out of contract at Stoke in the summer, having been at the Britannia Stadium since 2011.
West Brom will travel to West Ham later today, with Pulis having been confirmed as the new manager at the Hawthorns this morning. The Baggies sacked Alan Irvine this week after a run of seven defeats in nine league matches.
Could Stoke forward Crouch help solve their goalscoring problems?