Austin smashed a succession of club scoring records on his way to a 28-goal haul last season.
National newspaper reports on Tuesday claimed Premier League new-boys Hull were close to securing the 23-year-old's services but, while the Clarets acknowledge enquiries have been made over Austin, they insist the figures discussed fall well short of their valuation for the player.
A statement on Burnley's website read: "There have been reports from various media sources saying that Burnley FC are close to striking a deal for striker Charlie Austin. These reports are wide of the mark.
"Quite understandably there have been enquiries from a number of clubs but none have met Burnley's valuation of the player.
"Charlie Austin remains part of the squad of Burnley as we prepare for next season's matches."