Cole turned down an offer from Spurs in order to move to Merseyside last summer, but the switch has not worked well for the Londoner, who failed to establish himself as a first-team regular last season.
Reds manager Kenny Dalglish cast doubt on Cole's future at Anfield by bolstering his midfield this summer with the signings of Jordan Henderson and Stewart Downing, and the 29-year-old has not been deemed good enough for a place on the Scot's bench for the club's first two games of the campaign.
Redknapp, who signed Cole as a youngster when he was manager at West Ham, still believes the midfielder has the ability to excel in the top flight and could make a move for the player soon.
"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."
Redknapp is short of options in midfield after a series of injuries hit his squad.
Luka Modric is one midfielder Redknapp has not been able to play this season, with niggling ankle, groin and hamstring injuries the official reason why the wantaway playmaker has not been available.
Redknapp revealed on Monday that the 25-year-old has been unsettled by Chelsea's dogged pursuit of the player and was not included in the squad for the 3-0 defeat at Manchester United on Monday night as a result.
Modric did not train with his team-mates this morning, but could feature in Thursday's Europa League play-off second leg against Hearts despite the Londoners being 5-0 up from the first game.
That would drastically reduce the prospect of Modric moving to Chelsea as it would cup tie him for the Champions League group stages, but Redknapp could not care less.
"We are not in the Champions League so it won't affect us," the 64-year-old said.
"I'm not bothered about anyone else. He is here, we love him, he is a great player and I need him back playing.
"The chairman has made it clear that he is not for sale so he has to crack on with it now and I'm sure he will.
"Will he play tomorrow [Thursday]? Possibly. We will see how his hamstring is on Thursday. Certainly I'm looking to have him fit for the weekend against Man City.
"He is not going to go away and play for his country next week if he doesn't play for Tottenham, that's for sure, because he needs to play."
Chelsea are reported to have lodged a £30million bid for the player this week - their third of the summer - but Redknapp emphatically reiterated that the Croatian is not for sale.
"The chairman says he is not for sale. He has made that clear. "Yesterday [Tuesday] when I spoke to him he said that Luka definitely wasn't going and that was the end of the matter as far as he was concerned.
"I keep seeing that the chairman is trying to push the price up (for Modric).
"He is not trying to push the price up. He is not for sale. He has made that clear. He doesn't want to sell him."