Consider a shortlist that includes Diego Simeone and Sam Allardyce. It could be called eclectic. Or random. Atletico Madrid’s alchemist and ‘Big Sam’ may both argue they have been overachievers, but common denominators are so few and far between that for a club to consider both suggests they have an identity crisis.

Welcome to Everton, where the well-sourced news that their dream target was a double Champions League finalist followed suggestions a specialist at avoiding relegation had become the favourite to take over. Rarely has the gulf between ambition and actuality been bigger, rarely the sense of fear more apparent.

Because the noise emanating from Goodison Park is the sound of panic. Appointing Allardyce would be an indication that Everton were sufficiently spooked by the prospect of the drop that they would send an SOS to a manager who represents a guarantee of staying up.

Everton have been ever-presents in the top flight since 1954. Allardyce has managed in the top flight for 15 seasons, rarely with its largest clubs. His sides have never gone down. It is a remarkable record. It may also be an irrelevant one.

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Everton may have been in the bottom three before beating Watford on Sunday, they may have lost five games in a row until then, they may have a wildly imbalanced squad with a glaring need for a high-class centre-forward after the sold Romelu Lukaku was not replaced. But they are not bound for the Championship; not with Allardyce and not without.

And nor are they, sitting 15th in the Premier League, out of Europe after an ignominious group stage, in a position to lure one of the world’s most coveted coaches. The sense is that majority shareholder Farhad Moshiri does not require one reality check as much as two. The situation prompts questions if he joins the ranks of owners with plenty of ambition and money but insufficient judgment.

Because he does not need Allardyce’s firefighting skills. Clichés about being ‘too good to go down’ can be wrongly invoked. Not in this instance; Everton’s performance level has been low this season, their selection confused, their search for a strongest side and finest system a constant. Yet the calibre of footballer at Goodison Park means they need not play at anything like their optimum levels to still survive.

Consider the potential that has been untapped this season. Davy Klaassen and Sandro Ramirez generated impressive statistics abroad, but have done nothing in England. Any list of underachievers would have to include Ashley Williams, Gylfi Sigurdsson, Morgan Schneiderlin and Michael Keane. Kevin Mirallas, Aaron Lennon and Ademola Lookman may argue they have hardly had the chances to impress. Yannick Bolasie, Seamus Coleman, James McCarthy and Ross Barkley have not, because of injuries, but eventually each will be fit again. Between them, those 13 offer an opportunity to improve Everton. This is not the impossible job.

And in Allardyce’s defence, he has a capacity to get more from some players than his predecessors and successors: think of Lamine Kone, Wahbi Khazri and Jan Kirchhoff, catalysts when he kept Sunderland up. He tends to be popular with his players, is more tactically flexible than his critics would concede and usually brings a clarity of thought, which Everton have been lacking. He gets teams to keep clean sheets, and Everton have too few. He is very good at what he does.

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But the problem is what he does: avoid the drop, but with a brand of football that means there is a glass ceiling to what he can achieve and there are issues with the methods he deploys. Everton’s last two managers, Roberto Martinez and Ronald Koeman, have floundered in part because they did not understand the club or the fans’ expectations. Allardyce branded West Ham supporters “deluded” amid criticisms he did not play ‘the West Ham Way’. He once denied ‘the West Ham Way’ even existed.

It is easier to see why he would want Everton than they should choose him. Allardyce has long felt he is entitled to such an opportunity. His two biggest jobs have ended abruptly: Newcastle, where he was sacked after six months, and England, where he lasted a solitary game. He has felt wronged, slighted, pigeonholed. “I’m not suited to Bolton or Blackburn, I would be more suited to Inter Milan or Real Madrid,” he once said. Everton is the closest he will get to the Bernabeu. It is not another Sunderland or Crystal Palace, a club he will keep up, pocket the survival bonus and happily leave. It is a destination club for him; even they, if reports of a six-month deal are correct, realise he would only be a stopgap manager for them.

But he would leave Everton requiring a reboot, to play more attractive football after his spell in charge. That may be harder if too much money is spent on Allardyce-type players who will hardly help restore Everton to the top seven next season, let alone scale the heights Simeone has reached in Spain.

Going for Allardyce would suggest Moshiri has jettisoned his managerial model. Koeman was an imperfect choice but the idea behind his appointment was right. Now Thomas Tuchel would be an unrealistic target and Simeone more so. Other managers, such as Marco Silva and David Wagner, are employed elsewhere. But either now or next summer, the priority should be to secure an attainable manager with a progressive ethos, to make the sort of decision Tottenham did when appointing Mauricio Pochettino. Allardyce – almost two decades older, much more short-termist, with a more direct style of play and a greater reliance on the transfer market – represents his antithesis. Simeone represents a waste of time. Everton, neither as good a job as their owner seems to think or as bad a team as he seems to fear, need to get better at compiling shortlists.