The 23-year-old lost his place at the Amsterdam ArenA last season after new coach Ronald Koeman preferred to use American international John O'Brien.
De Cler was left out of Ajax's recent tour of Britain and is now known to be looking for a new club.
West Brom recently let former Coventry defender Marcus Hall go after a brief trial period with the club, so it is known that manager Gary Megson is on the look-out for a new left back.
Current incumbent Neil Clement is yet to pledge his future to the club and Megson wants to have quality cover.
De Cler has a proven record in De Eredivisie and could be the answer for the Baggies, should he impress over the next seven days.
