The Clarets chief is thought to be on a shortlist of candidates for the role at Goodison Park following the sacking of Ronald Koeman last month, with the Merseysiders reportedly keen to talk to Dyche.
The former Watford boss has done his part to distance himself from reports suggesting he could be tempted away from Burnley, a club he has helped establish in the Premier League during his time in charge.
Having kept the Lancashire outfit up last season, Dyche's men currently find themselves seventh in the Premier League table after an excellent start to the campaign.
Hendrick says Dyche has made life at Burnley extremely enjoyable and feels it would be tough to replicate the current working environment were he to leave for Everton.
"He [Dyche] has been great for us," Hendrick told Sky Sports News. "You never know what way a club can go if a new manager comes in or a manager leaves.
"We have got on well with him. We work hard every day. We enjoy going into training. That is the environment he has created there.
"But at the end of the day it is his decision. I am sure he has aspirations to go high in the game. He does talk about it himself and he is still a young manager.
"Obviously we would love to have him still at Burnley but it is his decision."