Redknapp believes the 28-year-old has already found a new club.
Cole is available on a free transfer as his contract with Chelsea expires this summer.
Manchester United, Arsenal and Spurs are among the clubs reportedly interested in Cole.
“It looks to me someone’s going to make a great free transfer, if he doesn’t stay at Chelsea,” Redknapp said.
“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.”