As Sportsmail revealed last weekend, Moyes was nearly certainly taking his last game in charge of the London club when he guided them to victory against Everton on Sunday. His current agreement ends in summer 2018.
Now sources close to the club have told me that Moyes is it is "more than likely" that the Scot will be thanked for his efforts but shown the exit door.
The Chilean cut his managerial teeth in South America with clubs such as San Lorenzo and River Plate before trying his luck in Europe with Villareal, Real Madrid and Malaga.
Rafa Benitez has been discussing his future as Newcastle United manager after guiding the club to 10th in the Premier League in their first season back in the division. He has been in China since 2016.
He took cost of Shakhtar Donetsk two years in the past in what was his first overseas job and gained the title in Ukraine in his opening two seasons, finishing a league and cup double in that first marketing campaign.
Allardyce, the former England and West Ham manager, was booed by visiting fans prior to Oumar Niasse making it 2-1 at the London Stadium, but there was to be no comeback.
West ham have discussed with the head coach of Shakhtar Paulo Fonseca prospects for his appointment as Manager of the English team, reports The Telegraph.
A number of other names have been linked with the vacancy in recent days, including Ronald Koeman, Carlo Ancelotti and Marcelo Bielsa.