The 28-year-old Northern Ireland forward, who was formerly at Leeds academy, travelled to Elland Road on Wednesday for contract negotiations.
Manager Simon Grayson said: "I spoke to a lot of players and he was one of them, but as it stands he will not be a Leeds United player. I've never been one for saying that he's been here or anything like that.
"I've spoke to the player, but I've spoke to another 10 or 15 other players. He's one of a few we have spoken to. Time will progress to see if we do anything."
It was believed that Hearts had been in contact with Feeney and that this could have been the reason why he would not be moving to Elland Road.
But it is believed that Hearts will not be pursuing the player either.