According to the Telegraph, the newly-promoted Baggies are hopeful of persuading Ivanovic, 36, to join them.
With no transfer fee involved, the two parties are at the stage of discussing personal terms.
Ivanovic is a free agent after leaving Zenit Saint Petersburg following three and a half seasons in Russia.
That no longer seems to be an option but Slaven Bilic is hoping to add his experience at West Brom.
West Brom have signed young players this summer, including Grady Diangana, Callum Robinson and Matheus Pereira.
But Bilic recognises the value of experience and Ivanovic is a proven Premier League defender.
The 105-time Serbian international spent nine years at Chelsea, winning three Premier League titles.