Benayoun is available on a free transfer after he was released by Chelsea, and representative Ronen Katzev has revealed that the Baggies are one of a number of clubs interested in sealing a deal for the 33-year-old.
Katzev told the Express & Star: "West Brom have registered their interest and now we are just waiting to see what other options are available.
"We have been negotiating with another club in the Premier League and clubs in Germany and Spain, so Yossi will have to make a decision very soon.
"He has been playing in England for a long time now so it has become like a second home to him."
The former West Ham United player made 13 appearances for Chelsea last season.