West Ham want to interview Manuel Pellegrini after Shakhtar Donetsk’s Paulo Fonseca ruled himself out of the running to replace David Moyes.

The club are hoping to make an appointment by the end of next week after Moyes told David Sullivan, West Ham’s co-owner, he was no longer interested in extending his stay at the London Stadium. The pair had been expected to meet next week but it is understood Moyes has decided to seek new opportunities after growing tired with his treatment.

The 55-year-old, whose six-month contract expired on Sunday night, believed he deserved a new deal after preserving West Ham’s Premier League status. Club officials were less sure and it became clear during the season’s final weeks they wanted to speak to other managers before reaching a decision.

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West Ham did not completely remove Moyes from their thinking, even while they were courting other managers. Sullivan hosted Fonseca and the agent, Jorge Mendes, at his Essex home on Monday afternoon and it is believed positive discussions took place during a 75-minute meeting. Sources had warned, however, that the Shakhtar manager was almost certainly using the talks to flush out better offers and it has since emerged the 45-year-old is expected to renew his contract with the Ukrainian champions.

Moyes had run out of patience and his decision to withdraw his candidacy has heightened the pressure on West Ham, who spent much of the season fighting against relegation. While they have indicated a desire to tackle the situation with a clear head, they are aware of the dangers of letting the vacancy remain unfilled for too long and would like to speak to Pellegrini, having already held informal talks with the Chilean.

The 64-year-old, who is in charge of Hebei China Fortune, is thought to be interested in a return to Europe. He knows the Premier League well, having led Manchester City to the title in 2014 and the former Real Madrid manager has an impressive pedigree. He is thought to be on a large salary in China and has also been linked with Sevilla.

West Ham also admire Newcastle’s Rafael Benítez, who was close to joining them when they replaced Sam Allardyce with Slaven Bilic three years ago. It it will not be easy to prise the Spaniard away from St James’ Park. Benítez’s contract, which has a year left to run, contains a £6m release clause and it is understood there would be additional compensation to pay.

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West Ham also hope to interview Unai Emery, who has been replaced by Thomas Tuchel at Paris Saint-Germain, while other candidates include Burnley’s Sean Dyche and Huddersfield’s David Wagner.

Moyes’s task was to pull West Ham out of the bottom three after replacing Bilic in November and he succeeded in difficult circumstances, finishing 13th. He inherited an unfit, unbalanced squad, received minimal backing in the January transfer window, saw Tony Henry leave as the club’s head of recruitment in January and watched as supporters mounted furious protests against the board during the 3-0 home defeat to Burnley in March.

Moyes managed to steady the ship and that calmness under pressure earned him the respect of one of West Ham’s owners, with David Gold backing him. Yet his relationship with David Sullivan was more fragile and both parties started to have misgivings during the season’s final weeks.

Moyes, who wanted greater control over transfers, adopted an increasingly bullish tone. He criticised West Ham’s culture of leaks, following his row with Andy Carroll earlier this month, challenged his employers to match his ambition and said the club had to make improvements off the pitch in order to become stronger on it. Yet he did not feel he had Sullivan’s trust.

He felt he could provide West Ham with stability and turn them into a top-eight club with the right backing. Now he is waiting for offers. His assistants, Alan Irvine, Stuart Pearce and Billy McKinlay, have also left.

Sullivan has targeted a replacement for Henry and is hopeful of appointing a director of football in the next fortnight.