"Carson is our first option," said the Liverpool manager, who has competition from Chelsea.
Both clubs have offered an initial £500k, but Leeds are demanding more up front.
"I first spoke to the Leeds manager two or three months ago and we're talking to the club because, with Jerzy (Dudek) and Chris (Kirkland), we need one goalkeeper for the future.
"Carson has the quality, though we'll have to see whether he has the experience. A week ago I was confident we would sign him, but now I don't know. He will play more games with us for sure. If I were him, I'd go to Liverpool because we've made it obvious we really want the player."
However, Norman Stubbs, the property developer hoping to takeover Leeds, has vowed to keep the 19-year-old U21 international at Elland Road.