The Baggies are understood to be making a big push for the 26-year-old, who is available after deciding to leave Aston Villa.
A host of clubs have been keeping tabs on him, with options both at home and abroad.
Paris Saint-Germain are the latest European heavyweight to take a keen interest in Reo-Coker, whilst the likes of Borussia Dortmund, Napoli and Valencia have all been looking at him.
In England, West Brom are now looking to head off interest from up to half-a-dozen Premier League rivals.
Baggies boss Roy Hodgson is looking for West Brom to push on next season and the signing of a player of Reo-Coker's calibre would be a clear sign of their intent.