Here, Press Association Sport looks at some possible names in the frame to replace the Croatian.
The Scot has been out of work since quitting Sunderland in May but is reportedly in pole position for the Hammers job. Moyes lost 28 of his 43 games in charge of the Black Cats and has won just 47 of his last 137 matches, including his spells at Manchester United and Real Sociedad. His stock has fallen dramatically since he left Everton in 2013 but West Ham could offer him the chance to rebuild his reputation.
It is staggering to think someone of Ancelotti’s pedigree is available, but he is. Bayern Munich cut ties with the Italian early in the season and, whoever gets the 58-year-old will get a man to have won three Champions Leagues and titles in Italy, France, England and Spain. The question is, would he fancy a Premier League relegation battle?
Another Premier League winner, Pellegrini is the current favourite for the job. He won the title with Manchester City in 2014 but left when Pep Guardiola became available. He is currently with Hebei China Fortune but, like Ancelotti, is a seasoned winner all over the world.
Coleman has yet to decide whether to pen a new deal with the Welsh Football Association after Wales missed out on the World Cup. His stock is high after taking Wales to the semi-finals of Euro 2016 and this could be a position to appeal to him.
Burnley’s boss celebrates his fifth anniversary at Turf Moor this month and continues to enhance his reputation as one of the finest English managers around. The Clarets have won promotion, twice, under his watch, and look on course to survive in the top flight for a second straight year after a strong start. That cannot have gone unnoticed further up the pyramid and though West Ham are beneath Burnley currently, their greater potential may tempt Dyche.