The Hammers have made a poor start to the new Premier League season and currently sit bottom of the table having lost their opening three matches.
It has been speculated that Bilic's position as manager was placed under review following the 3-0 defeat against Newcastle United in August and that he has little time left at the helm.
According to The Sun, the Hammers hierarchy are eager to dispense with Bilic and bring in Sarri, who has worked as a coach since 1990 and began at grassroots level.
The 58-year-old has managed 18 clubs during that time, most notably in recent years with Napoli and Empoli, whom he led to promotion from Serie B to the top flight.
Sarri has another two years left to run on his Napoli contract but is believed to have a buyout clause of around £7.5m.