His contract expired on Sunday night and while he is due to receive a healthy seven-figure bonus for keeping the club in the Premier League, it has become clear over the last few weeks that a lack of commitment from both sides was likely to lead to a parting of the ways.
The Scot steered West Ham to Premier League safety in a campaign capped by two goals from Manuel Lanzini and Marko Arnautovic's 11th of the league season.
Moyes said: "Everybody always thinks the grass is greener and there's something better out there".
"We've shown we're trying to improve. Confident? I can't quite say confident after all the rumours I'm reading in the paper", Allardyce said after a 3-1 defeat.
'I don't know if anybody can come and make that big a difference in six months.
Pochettino: Spurs must be fearless in transfer window
Goals from Jamie Vardy , Riyad Mahrez and Kelechi Iheanacho had put the Foxes into a 3-1 lead by the 47th minute at Wembley. Spurs battled through a poor performance to grind out a win in a game that was lacking in quality and spectacle.
"Bare in mind that Rafa Benitez came very, very close to taking the West Ham job, I think he'd nearly signed a contract to become the West Ham manager, before he was offered the Real Madrid job".
The same report that the board have held long-term interest in Newcastle United's Rafael Benitez, while Claret and Hugh claim the Spaniard is the club's top target for if Moyes does depart.
West Ham have wasted no time in searching for a replacement for David Moyes after meeting Shakhtar Donetsk manager Paulo Fonseca on Monday.
If he is their number one target, then action must be imminent, for they risk missing out the longer they wait. Confident? I can't quite say confident after all I'm reading in the paper.