The Daily Mail says Kewell is leaving Liverpool as an expensive flop, having cost almost £160,000 a game over five years since joining them from Leeds.
He made 138 appearances and scored just 16 goals after being signed by Gerard Houllier from Leeds for £5million in 2003 on a contract worth £60,000 a week.
Fulham, who attempted to sign him during the January transfer window, are almost certain to move for him again.
But Kewell will not accept an offer from Craven Cottage if they are relegated and is certain to attract a number of other clubs.