The Republic of Ireland international struggled to hold down a regular role at The Hawthorns last season and is understood to have grown increasingly frustrated at a lack of opportunities.
The Baggies are under new management, with Steve Clarke having replaced Roy Hodgson at the helm, but Cox is still facing up to an uncertain future.
Blackburn are already understood to have held talks with the 25-year-old striker, who formed part of Ireland's squad at Euro 2012.
Rovers have added Leon Best and Nuno Gomes to their attacking ranks this summer, but are seeking further firepower.
Celtic, however, are believed to have also entered the chase for Cox's signature and have already sounded out a deal.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.