Redknapp admits he is prepared to sign the midfielder, but has so far not made a move.
Cole turned down a move to Spurs 12 months ago in order to join Liverpool.
Redknapp signed Cole as a youngster when in charge at West Ham.
“I like Joe. I signed him as an 11-year-old. He is a good player,” said Redknapp.
“I’ve got all the time in the world for him.
“We haven’t made any enquiries about him but I wouldn’t sit here and say I wouldn’t have him at the club because if I did I’d be lying. I do like him.”
