Dyche was immediately seen as one of the frontrunners to take up the reins at Goodison Park when Ronald Koeman was relieved of his duties last week, and the Toffees' 2-0 defeat by Leicester City on Sunday (29 October) will only further calls for the former Watford boss to take over on Merseyside.
Dyche, who has performed tremendously during his five years in charge of Burnley, is certainly flavour of the month having overseen a wildly encouraging start to the season at Turf Moor, and though the 44-year-old knows his stock could fall in the blink of an eye if his side suffer a few poor results he did concede that reports linking him with Everton were "nice" to learn of.
"It's the yin and the yang. You get praise, but you lose three games and then you're getting slaughtered," Dyche told Sky Sports.
"I don't mean that in a precious way, it's just a fact, that's how quickly the shift occurs. You have managers out there who may have a tough streak, it doesn't make them a bad manager. They're just going through a tough spell.
"That can happen. So I don't read much in the media, I know what I've said so I don't keep checking up on things. There have been some nice things said recently, some nice links, but the fact is I'm still here and still working hard."
Dyche will want Burnley to avoid the start of a "tough spell" when they face high-flying Newcastle United on Monday [30 October] evening. Rafael Benitez's side have also enjoyed a rather positive start to the new campaign and find themselves ahead of Burnley in the Premier League table on 14 points. Both teams could climb into the top six with a win this evening, a position far from the reaches of Everton, who lie in the bottom three after suffering yet another defeat at the hands of Leicester.
Jamie Vardy's close-range finish and Jonjoe Kenny's unfortunate own goal handed the Foxes victory at the King Power Stadium in Claude Puel's first game in charge, leaving a sorry Everton to lick their wounds ahead of their Europa League clash with Lyon on Thursday.
Caretaker manager David Unsworth has made it clear that he would like to succeed Koeman at Everton, though his reign has interim boss has not gone swimmingly with two defeats from two games. Dyche is believed to be in the frame to take over, but majority shareholder Farhad Moshiri has set his sights on Watford manager Marco Silva and has reportedly made the Portuguese his number one target.