The Ivory Coast international is also wanted by West Ham, with the Upton Park outfit confident of sealing a £3 million deal for the 28-year-old.
|6/4||West Brom are 6/4 with Coral to be the top Midlands club
"We've stated an interest, we've had some negotiations and we're hopeful he'll come to West Brom," joint assistant manager Keith Downing told the Birmingham Mail.
The Baggies have yet to spend significantly this summer, with Nicolas Anelka and Diego Lugano joining on free transfers, and Downing says the club's plans to strengthen do not end with Kalou.
"We are still working to get players of his [Kalou's] ilk to come to the club," the coach continued.
"Discussions are going on. We know we have a good set of players, a good core and we have stated we are short in terms of numbers.
"We're aware of that but we know we need help. There is an importance now to get the two or three, maybe four, players in."