Allardyce, 63, sat down with Toffees chiefs in London this week to discuss the possibility of him replacing Ronald Koeman.
Farhad Moshiri, Everton’s major shareholder, has identified Allardyce as a leading candidate alongside Burnley’s Sean Dyche and Watford’s Marco Silva.
Talks with Big Sam’s camp remain ongoing and Allardyce has since spoken openly about the issues at Goodison Park – claiming the players have lost confidence and the club is in “a bad place”.
The former England boss told Paddy Power: “Everton are obviously in a bad place at the moment and, like every football club that is struggling, it’s mainly down to a loss of belief.
“The players’ loss of belief in themselves and their lack of confidence means that whoever becomes the manager of Everton, the first thing they need to do is re-instil that confidence and morale in them again.
“When a player plays with confidence, that’s when he’s playing to the best of his ability. At the minute, I can’t see that with that set of Everton players. It’s completely gone.
“At any football club, that should be your top goal and your main focus before anything else, keeping your team mentally happy.”
Everton are languishing second bottom of the Premier League with just two wins from their opening 10 games.
They spent £150million on their squad in the summer but their Europea League campaign is already over and morale is at an all-time low.
Allaradyce added: “There’s one simple reason why those players have no confidence left – results. Losing Romelu Lukaku, that team has found it more and more difficult to get the ball in the net. Points have been slipping past them without his 20+ goals.
“There’s no doubt that they can play just as well as their opposition, but they can’t finish teams off. They can’t score.
“And, because of that, the knock-on effect is pressure on the defenders, someone makes a mistake and then they lose games. Games that they should be winning, they’ve lost or drawn.
“The confidence has been drained from the players because of their bad results, and you can see that.
“I understand why they didn’t replace Lukaku – nowadays that’s such a hugely difficult piece of business. There’s such a lack of top quality strikers, not just in England but literally across the world today.
“But still, the club needs someone to get goals and change those results around.”