The 63-year-old was due to meet with major shareholder Farhad Moshiri at some stage this week where it was expected he would be informed that he will not be retained beyond the end of the current season.
Everton will then hope to conclude the arrival of PSV Eindhoven sporting director Marcel Brands as their new director of football, putting incumbent Steve Walsh's future role at the club into question.
Allardyce has had a meeting with Moshiri penned in for a few days but his confidence in remaining at Everton has been waining over the past few weeks.
Another season has come to a close, and for Everton, it was one that got off to a poor start before Sam Allardyce came in and steadied the ship.
Allardyce seemed to accept his fate after the Toffees' final match of the season, a 3-1 defeat by West Ham, on Sunday.
Forward of crunch talks with proprietor Farhad Moshiri, Allardyce mentioned: 'I cannot fairly say I am assured after all of the rumours I am studying as a result of, usually, there isn't a smoke with out hearth, is there?
Sam Allardyce is on the verge of leaving Everton Credit Action Images
With Everton seemingly in free-fall last autumn following the sacking of Ronald Koeman and amid David Unsworth's struggles to right the ship, Moshiri sounded out renowned Premier League firefighter, Allardyce, along with Silva and Fonseca as potential replacements.
"I can update you on the fact that all the rumours, gossip, miscalculations and stories the media are writing between me and Wayne are absolute rubbish", he told Sky Sports News.
Allardyce led the club to a respectable eighth-placed finish in the Premier League, however, he was criticized for a more defensive-minded style of play.
Silva was sacked by Watford in January following a downturn in results.
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