Former champions Leicester are looking for a new boss following the sacking of Craig Shakespeare, with Dyche among the favourites for the vacant role.
"He's been fantastic and long may it continue," said Mee, addressing Dyche's link with Leicester. "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.
"You can tell by his demeanour, nothing has changed for us. His mentality and focus is a strength for us.
"I've been here since he arrived and how far it's come has been massive. It's been five years and fair play to everyone for sticking with him, although there's been no reason not to stick with him, because he's done such a great job."