Makukula has struggled to make an impact at Benfica since a big-money move from Sevilla in January 2008, chalking up only three goals in 18 appearances for the Lisbon-based club.
Makukula said he still intends to leave Benfica, where he has failed to secure a regular place since Spanish coach Quique Flores took over this season, and is considering other offers.
Equally West Brom will be looking to explore other options to boost their strike-force.
The Baggies are bottom of the Premier League and in dire need of a reliable striker, having netted only 17 goals in 21 top-flight games this term, especially with frontman Ishmael Miller is out for the season because of a knee ligament injury.
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