The Toffees sacked Ronald Koeman last week following a poor start to the season in both the Premier League and Europa League.
Sky Sports News opened the day with the news that Everton were about to make an approach for the Burnley manager, but the Lancashire Evening Post hit back early with a morning (oddly) story that Dyche was not set to become Everton boss.
"When we talk about managers, we quite often talk about philosophies and values, but whenever you see this Burnley team, you have absolutely no doubt they're doing exactly what Dyche has told them to do, every single inch of the way".
Since joining Burnley in 2012, Dyche has experienced great success at Turf Moor, helping guide the club to two Premier League promotions - he is now the third longest serving manager in the division behind Arsene Wenger and Eddie Howe.
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Victory over Newcastle at Turf Moor on Monday evening could move Burnley up to sixth in the top-flight table, and the transformation they have experienced over five years under Dyche has not gone unnoticed by other clubs.
Realistically, Dyche is not going to be handed a top-six job so the opportunity to manage Everton can not be turned down.
"If you're in that Burnley boardroom - they're shrewd and they know what the cost is of going down - they might just be chucking a load of money at him and saying: "Give us seven more months, don't leave us without a manager for the rest of the season".
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"It's not something we are thinking about right now", he added. Sean Dyche won't go to a team in the Champions League in this country.
"Training is up there with the toughest I've had", Ward said. But respect has to be earned at all clubs and it has been earned here over a five-year period. If he stays, it'll be great for us. "We keep picking up points and there's no reason why we can't stay in the top half".
"We're not a recognised Premier League club yet, it doesn't just take a couple of seasons".
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