Speculation about his future has intensified amid reports the US-based Friedkin Group have been talking to potential successors after completing a takeover of the Liverpool club worth more than an estimated £400 million ($500 million) last month.
Everton have been ever present in the English top flight since 1954 but have flirted with relegation in recent seasons.
They are again battling to beat the drop this term, having won just one of their last 11 games -- a run that has left them in 16th place and one point above the drop zone.
Dyche, speaking at a pre-match press conference ahead of Everton's third-round FA Cup tie against third-tier Peterborough at Goodison Park on Thursday, was asked if he knew the club were considering his position.
"To be clear, it should be," he said.
Dyche added: "At the end of the day, if you're a business of this size, succession planning should surely be part of their diligence.
"I've got no problem with that at all. I think that should be ongoing at every football club. That's part of the business, surely. I'm sure it is in what we'd call normal business life outside of football... We've got to win games -- we haven't won enough this season."
But the former Burnley boss, who took charge almost two years ago, insisted he was still the man to turn things around.
"I am putting a lot of effort in and trying different ways and trying to work and look at all the different parameters on and off the pitch, the different ways of working," Dyche said.
"That's part of being a manager. I'm well versed in it."
