The Baggies hierarchy met with the former West Ham and Croatia manager on Tuesday evening, and he has now emerged as one of the main contenders for the role.
Chris Hughton and Chris Wilder are also still in the running, although Bruno Labbadia has fallen down the pecking order.
Bilic is out of work and available after being sacked from Saudi team Al-Ittihad in February.
The 50-year-old started his managerial career in his native Croatia with Hajduk Split, before becoming the national team manager for six years between 2006 and 2012.
He then managed Lokomotiv Moscow in Russia before joining Turkish club Besiktas.
Bilic is best-known in England for his time in charge of West Ham after that, where he spent just over two years between 2015 and 2017.
He guided the Hammers to a seventh place finish in the Premier League in his first season in England, earning them qualification to the Europa League.
West Ham finished 11th the season afterwards before a poor start to the 2017/18 season cost him his job.
After almost a year out of management, Bilic took over Al-Ittihad but only lasted five months.
Hughton, who was sacked by Brighton at the end of last season, is still in the running for the job.
It's believed he would have to take a pay cut from his previous Premier League salary to join the Baggies in the Championship.
Albion are still keeping tabs on Wilder's situation at Sheffield United, where an ongoing legal battle in the High Court between owners Kevin McCabe and Prince Abdullah of Saudi Arabia is causing tension.
The Baggies are ready to swoop for the LMA Manager of the Year if he decides to walk out of Bramall Lane.
However, that currently looks like being a long shot. Wilder is a Blades supporter, and has just won two promotions in three years to take United to the Premier League.
It's believed he's seeking reassurances from United's hierarchy about the transfer budget ahead of next season.