Dyche is among the contenders to take over at Goodison Park following the sacking of Ronald Koeman two weeks ago, although it is understood the club are still considering their options.
David Unsworth, Everton’s Under-23s manager, has been in charge of the first team for the last two matches, defeats at Chelsea in the Carabao Cup and Leicester in the Premier League.
He is expected to remain in charge when they take on Lyon in the Europa League tomorrow and host Watford on Sunday, after which there is an a break for international matches.
Sam Allardyce, who has been out of work since resigning as Crystal Palace manager in May, has indicated he would be interested in the Everton job.
He is one of the names being considered by the club, although he is not thought to be their first choice.
vCard.red is a free platform for creating a mobile-friendly digital business cards. You can easily create a vCard and generate a QR code for it, allowing others to scan and save your contact details instantly.
The platform allows you to display contact information, social media links, services, and products all in one shareable link. Optional features include appointment scheduling, WhatsApp-based storefronts, media galleries, and custom design options.
Dyche celebrated five years in charge at Burnley on Monday with a 1-0 home win over Newcastle that lifted his side to seventh in the top flight.
His success in transforming Burnley from a mid-table Championship club to one sitting in the top half of the Premier League has won him plenty of admirers, and he was a contender for the Leicester job last month before it went to Claude Puel.
That came just months after Dyche was linked with the role at Palace, with Frank de Boer instead getting the position before being sacked just four league matches into the season.
Garlick has made it clear he would love his manager to stay at Turf Moor for another five years, but is aware there is bound to be interest in him.
“That’s the price of success I guess,” said the Burnley chairman. “The more success we get, the more people are going to look at him. But we look after him well and we hope he’s going to be here for a long time.”
Dyche has a £2.5million buy-out clause in his contract and Garlick said the club were not yet looking for potential replacements.
“It’s not something we are thinking about right now,” he added. “There’s one person on our list and that’s Sean Dyche.
“We hope that continues for a long time, another five years hopefully.”
Dyche refused to rule himself out of the running for the Leicester job before it went to Puel, and it is understood he would be interested in the right opportunity to move on.
Burnley’s players have made it clear they want Dyche to stay, having enjoyed a series of impressive results this season.
They have gathered eight points from their first five away matches, with wins at champions Chelsea and Everton as well as draws at Liverpool and Tottenham.
Defender Matt Lowton has suggested the club are more than capable of finishing in the top half of the Premier League if they continue their momentum.
Lowton said: “The gaffer’s done a great job since he’s been here. Everybody knows that and it’s up to us as players to keep going and get the results as a team and a squad.
“It’s been a fantastic start. We’ve given ourselves a great platform to move on throughout the season. We keep picking up points and there’s no reason why we can’t stay in the top half.”
Midfielder Jeff Hendrick added: “I’ve enjoyed working for him. I’ve been here just over a year and I’ve enjoyed every moment.
“We work hard during the week but that’s the bare minimum he wants on a match-day and then he gives us that freedom to go and play football.”