The Hammers went into Friday's huge clash with Brighton and Hove Albion needing a home win, but Bilic saw his side capitulate in a shambolic 3-0 defeat at the London Stadium.
That's now five defeats in the first nine league games of the season for Bilic, and the Croatian – who only just about managed to cling onto his job at the end of last term – is again under huge pressure.
Speculation has surrounded Bilic's future for weeks, but the manner of Friday's defeat has many believing that Bilic's tenure in East London is about to come to a crushing end.
The Telegraph report that West Ham are already considering alternatives, and whilst Huddersfield Town boss David Wagner is their top target right now, they are also pursuing Manuel Pellegrini.
Pellegrini, 64, is best known for his time with Manchester City, where he won one Premier League title in his three years with the club, winning 100 of his 167 games in charge.
The Chilean moved on to China with Hebei China Fortune in 2016, but it's believed that his lucrative contract in the Far East could be a major stumbling block as West Ham pursue his signature.
Formerly of Villarreal, Real Madrid and Malaga, Pellegrini has often impressed over the course of his career, but West Ham may face a struggle meeting his demands and outlining their challenge, given that Pellegrini has already won the Premier League title once, and it's unclear just what West Ham are aiming for.