"It was a move where the easy option was to stay in London, but he went for it and headed north. I said then I wished him all the best. I signed Joe when he was 11 years old. I've seen him grow up, and I've got all the time in the world for him."
Redknapp revealed that signing Cole would have been at the expense of Rafael Van der Vaart, who has made a huge impact since being snapped up from Real Madrid.
"Joe could have come here and been fantastic for us, you never know," he said.
"But, no, we wouldn't have taken Rafa had we taken Joe and, let's be fair, Rafa has done great.
"It's early days for Joe at Anfield. Roy had a difficult start and now he's settling in. They'll turn the club around. They've got a new owner, who looks like he's got fortunes. The future should be good."