It is understood that the Australian international rejected a new contract on reduced wages after an injury-hit time at Anfield.
Boss Rafael Benitez said: "We have tried to come to an agreement with the player and his agent, but that has not been possible.
"Kewell will leave the club at the end of his contract."
Benitez also slapped a £15m price tag on striker Peter Crouch and revealed he had held talks with Aston Villa about Bareth Barry.
He said: "I have spoken to Martin O'Neill, he knows my ideas.
"But we agreed to wait until the end of the season for any more discussions."
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