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.
Now the Spurs boss has revealed his desire to lure the former West Ham player to north London.
He told the Daily Express: "Yes, I am prepared to declare my interest in Joe Cole.
"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."