It has been reported that England Under-19 international Cook, who signed a new two-year deal last May, has a clause in his current deal allowing him to leave Leeds for £5m if the club are not promoted this season.
But Leeds said in a statement on their club website: "Leeds United would like to categorically deny reports that have emerged in the local press this morning (Thursday) regarding a supposed release clause in the contract of Lewis Cook.
"The claim by the Yorkshire Evening Post, which the club feels was published with damaging intentions, is entirely inaccurate and unfair reporting.
"No release clause whatsoever exists in the contract of the player in question."
Cook, 19, has attracted interest from a host of Premier League clubs since making the first-team breakthrough last season.
Leeds turned down an approach from Bournemouth in January and there are fears among fans that Cook could soon follow Sam Byram out of Elland Road after the defender joined West Ham for a reported fee of £3.7m in January.