Everton said in a statement: "Sam Allardyce will be at USM Finch Farm this afternoon to finalise terms on becoming the new manager of Everton Football Club".
The Goodison club has now confirmed on their official Twitter account that the ex-England boss is on the verge of being appointed as manager but David Unsworth will remain in charge against the Hammers on Wednesday.
David Unsworth has encouraged the public to give the next manager of Everton time and patience to build the club.
Sam Allardyce wants Sammy Lee to join his coaching setup at Everton.. But the chance to turn around Everton's faltering ship has lured him back, and Allardyce is expected to have a watching brief at Goodison Park on Wednesday night.
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Allardyce returns to club management six months after resigning from Crystal Palace, having saved the London side from relegation.
Everton now sit one place above the Premier League relegation zone after 13 games, having lost four of their last seven league games. But they have lost their last two matches 5-1 to Atalanta and 4-1 against Southampton, taking the tally of goals Everton have conceded this season in all competitions to 46.
The 63-year-old will manage his first match when Everton host Huddersfield Town on Saturday.
The Toffees spent more than £130m on new players in the summer but have struggled without last season's top scorer Romelu Lukaku, who was sold to Manchester United for £75m in July.