As for Laws, he insists neither he nor the players will be affected and that he is experienced enough to cope.
Laws said: "There's no foundation to it, whether it's a ploy to destabilise us I don't know but we have put the lid on it very firmly.
"It was totally wrong, there was no truth in it whatsoever and the chairman has been very clear about that with a strong message.
"We have a long-term plan here, we are not looking at the short term and he has deliberately gone out there to slam it down.
"This was uncalled for and the good thing is it won't affect the players.
"Whatever knocks come our way we are big enough and strong enough to take them and I have been in the game long enough to have a thick enough skin to not let that affect me.
"I certainly won't be walking around with a grimace on my face or my head down, but working as hard as ever to prove the knockers wrong."
The Clarets have dropped into the relegation zone since Laws was brought in to replace Owen Coyle after he left to manage Bolton, but Kilby has insisted they are not considering a change.
Burnley could take a big step towards easing the pressure on their shoulders with a win at Wigan on Saturday but that would mean ending an appalling away record this season of 14 defeats and one draw, without a single win in the league.
Laws will be able to call on Steven Fletcher who has missed the last three games with a broken hand.
"The thing we were desperate for was to have Fletcher back and he has been training this week," said the Burnley manager.
"He's got the green light to start playing again and that is a real bonus for us as he's real quality and has got goals in him."
Steven Caldwell and Chris McCann are unavailable but Danny Fox is in the squad despite being taken to hospital after the Wolves match with a suspected broken rib.
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