England centre-back Keane, 24, continues to be linked to the likes of Liverpool, Manchester United and Everton after a stellar season in which he was nominated for the PFA Young Player of the Year award and made his international bow.
Keane’s deal at Turf Moor expires next summer but Dyche has already stressed that the Clarets would be willing to let him run that down rather than offload him on the cheap at the end of this campaign.
Burnley’s hand has been strengthened by Dyche’s team all but securing their top-flight status last weekend and their position of financial stability is why their manager would be unperturbed around any negotiating table.
“It’s been ongoing all season,” Dyche told talkSPORT. “You want your players to be successful – it’s good for them, good for the team – on the other hand that does bring interest. It’s something we’ve become used to.
“We’ve had people talking about our players every year, it’s a natural challenge for a club like this because we’re not one of the superpowers of the division. Players eventually will outgrow us, move on or be hunted, it’s just the way it goes.
“We’re a club that’s in unbelievably healthy shape so there’s certainly no pressure to do anything. It’s more a case of what’s right. If all parties agree then that might be something the club will have to look at just by the realities of what it is in the Premier League.
“We’re certainly in very healthy shape and don’t have to make any decisions for any reason other than we think it’s appropriate.”