Hoyle, who appointed Clark at Huddersfield 13 months ago, said: "It's flattering that both our players and manager are being linked to other clubs because it's a reflection of how far we've come. Rumours are part and parcel of football."
Hoyle added: "I saw the story on Sky Sports News on Sunday and was very surprised, as far as I'm concerned, there's no truth in it.
"There hasn't been any approach from Burnley regarding Lee. I have an open and honest relationship with Lee, we talk all the time, but we've never spoken about this."