United were reported to be keen on Hart, who guided Forest to the play-offs last season, to replace Peter Reid in November.
A statement on the club's official website read: "Leeds United can confirm that they will not be discussing the managerial position with Paul Hart.
"Eddie Gray has been granted a further extension to carry on as Leeds manager for the rest of the season and the board is standing by that decision."
Forest sacked Hart after they slipped into the Division One relegation zone after their home defeat against Coventry City yesterday.