The Israel international has been released by Chelsea this summer following three years at Stamford Bridge and is now considering his options.
He has also previously played for West Ham United, Liverpool and Arsenal, and has become accustomed to life in England.
Benayoun's representative, Ronen Katzev, says there are a couple of clubs keen to keep him in the Premier League and claims that he is on West Brom's radar.
However, there is also interest from Germany and the 33-year-old does not want to rush into making a decision.
Katzev said: "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."