Bilic is seen as a dead man walking after The Hammers slumped to the bottom of the Premier League table after losing their opening three games of the new season.
West Ham visit Premier League new boys Huddersfield tomorrow night with time running out for Bilic who survived crisis talks two weeks ago.
The Croat blasted chairman Dave Sullivan on Friday for claiming he turned down the chance to sign Renato Sanches and Grzegorz Krychowiak on deadline day.
It was a clear sign that Bilic, who is out of contract at the end of the season, feels that his time at the London Stadium is coming to an end.
Newcastle boss Rafa Benitez was the early favourite for the job but it appears that he will be staying at St James’ Park for the immediate future.
Sullivan and co owner David Gold have now got Sarri in their sights who spent a decade coaching a series of grassroots clubs in Tuscany before getting his big chance with Napoli.
The 58 year-old ironically replaced Benitez at the Italian club and even though he is relatively unknown in this country he is seen as being one of the best tacticians in Italian football.
Sarri has another two years left to run on his Napoli contract but has a buy out clause of around £7.5 million which is well within the Hammers’ price range.