Former Manchester City manager Manuel Pellegrini has emerged as the front runner for the West Ham job.
The Irons plan to have a new manager in place within 10 days after opting not to keep David Moyes on.
The Scot's short-term contract ended at midnight on Sunday after West Ham's final game of the season, a 3-1 win over his former side Everton which saw them finish 13th in the Premier League.
Joint-chairman David Sullivan said the club needed to move in a "different direction" with a "high-calibre figure".
With Portuguese coach Paulo Fonseca having signed a new contract at Shakhtar Donetsk, it now appears West Ham's attentions have switched to Pellegrini, with Newcastle boss Rafael Benitez also having been linked with the vacancy.
West Ham would not comment on the reports emerging from Chile that Pellegrini, currently in charge of Hebei China Fortune, was set to be offered the job at the London Stadium.
West Ham Manager First League Game 2018/19 Season (odds via Sky Bet)
- Manuel Pellegrini - 1/5
- Rafael Benitez - 11/4
- Claudio Ranieri - 5/1
- Unai Emery - 16/1
- Eddie Howe - 20/1
Pellegrini coached at Villarreal, Real Madrid and Malaga before joining taking charge of Manchester City in 2013, going on to win the 2013/14 Premier League title as well as the League Cup twice before his departure.
The Chilean left the Ethiad Stadium in June 2016, where he was succeeded by Pep Guardiola, but was soon back in work at Chinese Super League side Hebei China Fortune.
Reports originating from his homeland claim Pellegrini, 64, is set to travel to London over the weekend for further talks, with initial contact having taken place via representatives.
It has been suggested West Ham would need to meet the seven million US Dollars (£5.3m) release clause with Hebei China Fortune as Pellegrini's current contract runs through to the end of 2018.
Assistant coaches Alan Irvine, Stuart Pearce and Billy McKinlay have also all left the London Stadium, allowing the new manager a clean slate.
Hammers joint-chairman Sullivan said on Thursday: "We are already taking steps to identify and recruit the manager we believe can take West Ham United forward in line with our ambitions."
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Odds correct at 1515 BST (18/05/18)