Ivanovic is a free agent after leaving Russian side Zenit Saint Petersburg at the end of last season.
The 36-year-old Serbia defender previously spent nine years in England with Chelsea where he won three Premier League titles, three FA Cups, one League Cup, one Europa League and the 2012 UEFA Champions League.
Ivanovic joined Zenit from Chelsea in January 2017 and won two league titles and one Russian Cup at the Gazprom Arena.
Ivanovic is expected to sign a one-year contract at the Hawthorns, with Bilic confirming his imminent arrival on Friday.
"It's very close. Hopefully it will be done later, in a matter of hours,” Bilic told reporters.
"He would be a great addition for us, a team who is newly promoted in the Premier League. He ticks all the boxes for us.
"He's done everything in his career - it's been magnificent. We'd be delighted. First of all, he will add quality, also his experience on the pitch and off the pitch.
"So it is not only him, it is him plus the influence he will have on not just defenders but the whole team around him. That's why we targeted him as one of our prime targets. It would be a great signing for us."
West Brom will host Leicester City in their first game of the season on Sunday.
