Casillas called Cole the "best left back in the world", and said the 29-year-old is desperate for a "clean break" from his troubled life in England.
Cole is being tipped for a £30 million exit from Chelsea, to join former boss Jose Mourinho at the Bernabeu.
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"From what I am hearing the signs look good. I have only briefly spoken to people at the club but I am confident that he can be a Real Madrid player next year. I think it will be the right move for him both professionally and personally," Casillas said.
"It will be his last big contract and who better to sign for than his old coach Mourinho at Real. He will know better than anybody this club will be successful under Jose."
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Elswhere, The Sun reports that Harry Redknapp is on the verge of completing a deal for Seville and Brazil striker Luis Fabiano.
Spurs are also continuing to court Joe Cole, who remains a free agent after leaving Chelsea.
The Daily Mail claims Portsmouth will withdraw their offer of a player-coach role to David James if he doesn't accept sometime today.
Source: DSG
