Roberto Martínez’s position as Everton manager will be discussed this week by the club’s board of directors, with the Catalan struggling to save his three‑year tenure at Goodison Park.

Martínez, 42, insisted he was the right man for the job and that Everton were close to challenging for trophies after their stoppage-time defeat by Manchester United in the FA Cup semi-final on Saturday. But with dissent growing among some of the supporters, Everton directors will convene to discuss the manager’s future.

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Everton’s chairman, Bill Kenwright, is renowned for his loyalty towards managers and was filmed speaking in glowing terms about Martínez before the semi-final at Wembley. But Kenwright is no longer the club’s major shareholder after the British-Iranian billionaire Farhad Moshiri acquired a 49.9% stake in February and changed the make-up of the Goodison board.

Moshiri is not an Everton director but has appointed a long-term associate, the financier Alexander Ryazantsev, as his representative on the board. The chief executive, Robert Elstone, also became an Everton director after Moshiri’s investment and along with the long-time director Jon Woods and Kenwright, they will hold talks over the manager’s future before the Premier League game against Bournemouth on Saturday. Woods left his seat in the directors’ box at Anfield in the 60th minute of the 4-0 defeat against Liverpool last week.

Martínez had admitted the Merseyside derby and United Cup tie amounted to a defining week for Everton and it yielded a shambolic display at Anfield followed by a second semi-final defeat of the campaign. With the team 11th in the Premier League, having won only nine of 34 matches and recorded Everton’s lowest points total at Goodison on the basis of three points for a win, the manager has been subject to angry protests in recent weeks.

Martínez is, at this stage, expected to be in charge for Bournemouth’s visit for what may become a divisive occasion. Some fans have taken to social media to propose various forms of protests at Goodison such as a mass walk-out or waving white handkerchiefs, the traditional show of disapproval in Spain.