Bilic, 52, signed a two-year contract when he took over at the The Hawthorns in June 2019, replacing Darren Moore.
He guided Albion to promotion on the final day of last season, as they finished second in the Championship.
But they have won only one Premier League match this season, beating bottom club Sheffield United 1-0 on 28 November.
It emerged after the draw at Manchester City that West Brom were considering whether to sack Bilic.
Tuesday's match was the Croat's 100th Premier League game as a manager. He led West Ham from June 2015 to November 2017, taking the club into a Europe as they finished seventh in his final full season, recording their highest placing since 2002.
Prior to that, he had led Croatia to two European Championships, with a quarter-final appearance in 2008 coming after they had knocked England out in the qualifiers.
He has also had spells in charge of Hajduk Split, Lokomotiv Moscow, Besiktas and Al-Ittihad.
Sam Allardyce, Nigel Pearson, Mark Hughes and Eddie Howe are all reportedly candidates to replace Bilic.
Allardyce has been out of work since leaving Everton in the summer of 2018, while Hughes left Southampton later the same year.
Pearson, who is a former Albion caretaker-manager, had a 20-game spell at Watford last term, while Howe left Bournemouth in August after his side were relegated from the Premier League.
Analysis
BBC Sport's Simon Stone
Slaven Bilic and his staff were informed of the news this morning in a face-to-face meeting. It is understood that the discussion was amicable but after collecting seven points from 13 games, the club had no confidence that the situation could be turned around in the short term to allow them to preserve their Premier League status. The club regard the way the news leaked out on Tuesday night as unfortunate; it was not the way it was intended to be communicated.
https://www.bbc.com/sport/football/55253670
