Rodriguez, 27, was a Pulis target in the summer but Southampton opted to keep him after promising him first-team opportunities under Claude Puel.

But the England international has started only one Premier League game this season and Pulis is keen to take him to the Hawthorns to strengthen his depleted attack.

Salomon Rondon and Hal Robson-Kanu have been the only senior strikers available to West Brom for months, with Saido Berahino struggling with form and fitness and Rickie Lambert having left for Cardiff.