"Leeds confirm they are in talks with Nick over his future with the club," said a statement on the official club website. "Discussions are under way with regard to the early termination of his contract," it added.
And it said that they hope to conclude the matter by the end of the week.
Hull City have confirmed their interest in Barmby with Hull chairman Adam Pearson telling the Yorkshire Post: "We understand Nicky is interested in coming to play for Hull City and he is certainly a player who, if he is available, we will have a look at to see if he fits in with our current structure.
"We are not prepared, however, to break the current level of pay. We are strict on that point so we will need to see what can be done.
"Nicky being handed a free transfer at Leeds is certainly an interesting development and we owe it to ourselves and our supporters to investigate any options open to us. We will be keeping an eye on developments."