Mee has revealed that the speculation has been addressed by Dyche, but acknowledged that the club's "fantastic" boss will inevitably attract interest from elsewhere.
The 28-year-old is quoted by The Mirror as saying: ""He's been fantastic and long may it continue. He's spoken about it and he's focused on us. We look forward to having him here.
"He's been linked with jobs four or five times recently because he's doing such a good job here. He's bound to get some attention, that's the way it goes.
"He's been massive for us, but we still want to keep growing as a club. It's been a massive change and hopefully he won't go just yet."
Dyche has won 91 of his 229 games in charge of Burnley since being appointed as manager in October 2012.