Chelsea announced on Wednesday morning that Cole will leave Stamford Bridge along with fellow midfielder Michael Ballack when their current contracts run out at the end of the month.
Redknapp gave Cole his top-flight debut with West Ham more than a decade ago, and has confirmed his interest in teaming up with him again.
He told talkSPORT that he has been in touch with Cole, but says the player won't make a decision on his future until after the World Cup.
When asked about the chances of Cole joining Spurs, he said: "It's not impossible. I think that Daniel [Levy], the chairman, has spoken to Joe's agent and he said that Joe didn't want to discuss any moves until after the World Cup. Then he's going to look at his options.
"But he's told us that he hasn't decided anything yet and he hasn't done anything definite. So there's a chance. I suppose it all depends on the financial side of it and everything else, but according to his agent he's not made up his mind yet."