The Frenchman, 35, who cost Madrid £46m in July 2001, said: "They are ready to pay more than they did for me - and this will lift the weight from my shoulders.
"He had a great season and I think the fact that he and Portugal got knocked out at the quarter-finals doesn't mean anything because they were up against a great Germany team.
"He is not scared of his new Real Madrid engagement and every time they wanted good players they got them.
"Now it depends on his personal plans. If he wants to play there he will play there."