Dyche secured a top-flight return for the Lancashire side by leading his team to a second-place finish in the Championship last season.
Burnley have subsequently begun the process of adding to their squad with the likes of Matt Gilks, Steven Reid and Marvin Sordell having moved to Turf Moor.
Speculation has now linked Burnley with a move for Deeney, who has bagged 44 league goals over the past two seasons.
However, Dyche stated that, while he admires Deeney's talent, Burnley cannot afford to shell out huge sums of cash on one player.
"Yes. The latest one is [that we will sign Deeney for] £8 million," he told Sky Sports News. "I am not sure where they have got that from and I don't know what club they think we are.
"He is among many players I admire but we have a certain brief. We can't spend £8m on players, I assure you."
