Reo-Coker is able to join a Premier League club outside of the transfer window as he is currently a free agent, but only if they have space in their 25 man squad which the Baggies do.
The midfield enforcer has been without a club since rejecting a short term deal to stay on at Championship club Ipswich last month and it was thought that another second tier side would come in for him.
However it seems Clarke is looking to add another face to his midfield after youngster George Thorne was ruled out for the remainder of the season with knee ligament damage that he suffered against Everton in midweek.
Reo-Coker was West Ham captain when they finished in the top half of the Premier League in 2006 and the 28 year old has also enjoyed spells with Aston Villa and Bolton since then.
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