The 36-year-old, who can play as a right-back or center-back, is a lazy agent after leaving the Russian St. Petersburg Zenit this summer.
Ivanovic would bring a great deal of Premier League delight to the newly promoted Baggies, having won the name three times with Chelsea, for whom he has played nearly 400 appearances in nine years at Stamford Bridge.
The Serbian foreigner is undergoing a medical examination on the West Brom floor and Bilic said: “It’s very close. I hope it’s done later, in a few hours. “
“It would be a wonderful addition for us, a team that has been promoted to the Premier League. He meets all the requirements for us.
“He’s done everything in his career, he’s been magnificent. We’d love to. First, you’ll raise the quality, as well as your delight on and off the field.
“So it’s not just him, it’s him plus the influence he’ll have not only on the defenders, but on the whole team around him. That’s why we’ve pointed it out as one of our main goals. It would be a wonderful signing for us. “
Since leaving Chelsea, Ivanovic has spent the last three and a half years at Zenit, where he won two league titles and one Russian Cup, and is expected to sign a one-year contract with the Baggies.
Bilic also showed that he will point out to midfielder Filip Krovinovic an indefinite contract with Benfica, following the 25-year era of loan at the Hawthorns last season.
“In addition to the new recruits, we’re also looking to keep last season’s players on loan, the ones we’re looking for,” Baggies said.
“We have pointed out Grady (Diangana) and Callum Robinson and we are doing everything we can to point out Krovinovic as well. This is easy to do, especially in cases of coronavirus.
“It’s not easy to locate the players you want, however, we check and hope to be able to do so. “