Cole, who scored in England's 3-0 World Cup warm-up victory against Platinum Stars on Monday, is out of contract at Chelsea this summer and has been linked with a number of clubs, notably Spurs, Arsenal and Manchester United.
"Yes, I am prepared to declare my interest in Joe Cole," the Spurs boss told the Daily Express.
"Why not? He is a great player, his contract is up and he is on a free transfer.
"When he returns I would love to talk to him about coming to Spurs."
Redknapp's statement contradicts his comments last week when he claimed he believed the 28-year-old would leave Stamford Bridge this summer but his destination would be somewhere other than Tottenham.
"It looks to me someone's going to make a great free transfer, if he doesn't stay at Chelsea,'' Redknapp had told BBC Radio 5 Live.
"I genuinely don't know who that is. I don't think it's going to be Tottenham. I've got a feeling, I may be wrong, that he's already agreed a deal with someone, and it's not Tottenham.
"I'm not saying if he hadn't agreed a deal with someone and he was available and didn't stay at Chelsea that we wouldn't be interested.
"I'm a big fan of Joe's, but the feedback we've had is that he might well have already done something.''