Dyche guided his side to a 1-0 victory over Newcastle tonight to lift them up to seventh in the Premier League table.
The 46-year-old has worked wonders in his five years in charge of the east Lancashire side, earning two promotions and establishing the Clarets in the top flight.
But Dyche is second-favourite with the bookmakers to take over at Goodison Park – behind only Ex-England and Bolton manager Sam Allardyce.
And after tonight’s victory over the Magpies, Dyche had his say on the speculation linking him with a move to Merseyside.
“We just keep getting on with it,” Dyche said.
Sean Dyche has not ruled out a move to Everton
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I just keep getting on with my job – it’s as simple as that.
Sean Dyche speaking after Burnley beat Newcastle 1-0
“We have to plan in the board room. We take each game as it comes, process the information after them and keep that clarity of thought.
“I just keep getting on with my job – it’s as simple as that.”
Everton sacked Ronald Koeman last week with the club lamented in the relegation zone.
David Unsworth has been placed in temporary charge of the Toffees while chairman Bill Kenwright hunts for the right candidate.
Jeff Hendrick scored the only goal as Burnley beat Newcastle
And if he chooses to pursue Dyche, ex-Liverpool defender Jamie Carragher thinks he would be stupid to turn it down.
Carragher said: "If he has been, or gets offered the Everton job, he has to take it. He has to.
“Maybe Burnley fans don't want to hear that, but he has to.
“Sean Dyche won't go to a team in the Champions League in this country. Everton are the next step.”