West Ham have started to identify potential replacements for Manuel Pellegrini, who is fighting to save his job after his struggling side’s 3-2 defeat by Tottenham on Saturday, and could alleviate their goalkeeping crisis by signing Jordan Archer on a free transfer in January.

Pellegrini is under pressure after seven games without a win and there is alarm at board level about a decline that has left West Ham three points above the bottom three. While there is a desire to give the 66-year-old time, the hierarchy’s faith in a manager who has 18 months remaining on a contract worth £7m a year is being severely tested at the moment.

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West Ham fear they are being dragged into a relegation battle and they are prepared to act if there is no sign of Pellegrini improving the situation. The manager was warned on Sunday that results must improve. Tentative overtures have been made to Rafael Benítez, who joined the Chinese side Dalian Yifang last summer, but Chris Hughton is emerging as a more realistic candidate. Hughton, who has been out of work since being fired by Brighton at the end of last season, would be interested in taking over if the job becomes available.

West Ham, who were torn apart by Tottenham at the London Stadium, have long admired Benítez. They were close to appointing the Spaniard before he joined Real Madrid in 2015 and attempted to lure him away from Newcastle before hiring Pellegrini last year. Benítez has maintained a good relationship with David Sullivan, West Ham’s co-owner.

Financial imperatives will complicate any move for the former Liverpool manager, though. Pellegrini will receive hefty compensation if he is dismissed midway through a deal that runs out at the end of next season and West Ham would have to pay a considerable sum to recruit Benítez, who is earning a reported £12m a year in China.

That is likely to make West Ham look elsewhere and it is understood that Hughton, who kept Brighton in the Premier League after taking them up in 2017, has admirers at the London Stadium.

Facebook Twitter Pinterest Chris Hughton, the former Brighton manager, is well regarded within the West Ham hierarchy. Photograph: Daniel Leal-Olivas/AFP/Getty Images

Bournemouth’s Eddie Howe is also under consideration and it is understood that Burnley’s Sean Dyche would be interested in speaking to the east London club.

West Ham’s goalkeeping situation could also make them hold off replacing Pellegrini. Lukasz Fabianski has been sorely missed since suffering a hip injury in September and the former Swansea goalkeeper’s absence has been exacerbated by calamitous performances from his deputy, Roberto, who had another poor game against Tottenham. There is a feeling that a new manager would struggle to make an instant impact if he has to use Roberto.

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With no date given for Fabianski’s return, West Ham will try to sign a goalkeeper in January. They are looking at Archer, who has been without a club since leaving Millwall at the end of last season. The 26-year-old Scot started his career at Tottenham.

The question for now is whether Pellegrini picks Roberto over David Martin when West Ham visit Chelsea on Saturday. Roberto’s erratic displays have damaged the team’s confidence and the decision to sign the Spaniard on a free last summer has raised doubts over the judgment of Pellegrini and Mario Husillos, West Ham’s director of football.