Redknapp confirmed his interest in the want-away England international this morning.
"I'd be lying if I sat here and said I wouldn't have Joe Cole at the club," he said.
Cole is keen on a return to London and has also been linked with QPR.
Redknapp also said: "I like Joe. I signed him as an 11-year-old. He is a good player.
"I've got all the time in the world for him."