Speaking on his club's official website, Forest chairman Nigel Doughty said: "We are all aware of the intense speculation linking our manager Paul Hart with Leeds United and I would like to explain our feelings on this issue.
"As Chairman of the Club I think I speak for everyone connected with us in saying that I would very much like Paul and his backroom team to stay on at The City Ground and continue the excellent job they have done in the last two and a half years.
"We cannot prevent speculation in the media and it is something that all Clubs with successful managers have to live with from time to time.
"In years gone by I am reliably informed that during his time with us Brian Clough was continually linked with every conceivable managerial vacancy that arose.
"Paul is halfway through a five-year plan with Nottingham Forest and throughout that time has made measured progress in search of our ambition to return to the Premier League.
"It is a fact because of injuries and illness we might not be doing as well as we would like at the moment but there is no doubt in my mind that it is merely a little dip that all clubs experience at some stage."
Hart himself told the BBC he had heard nothing from Leeds: "There has been no contact whatsoever. I don't really want to comment on it. That is for other people to do. I'm manager of Nottingham Forest as far as I know and I can only talk about Forest."