In the second part of a serialisation of his forthcoming autobiography, Redknapp has revealed in the Daily Mail the part he played in transforming Bale from a talented young player to the superstar he is today.
He managed Bale during his time in charge of Tottenham Hotspur and insists he never had any doubts about his ability, although it was necessary to toughen him up.
Redknapp said: "There is some right old rubbish talked about Gareth Bale's time with me at Tottenham. Was I ever going to sell Bale? No. Was I going to loan him? No.
"Whatever faults I may have, I do know a player. I would never sell Gareth. All he needed was to be toughened up to emerge as a star player.
"We had to tease that combative streak out of him because, at that time, he was regarded as a left-back and was up against Benoit Assou-Ekotto, one of the best in the Premier League. Gareth seemed too soft to be a defender so we decided to try him further forward.
"He drove me mad in training. Technically, he was outstanding but he always seemed to be playing with his hair. It was never right. He'd be flicking the fringe or wiping it out of his eyes and I would be going quietly mad, just watching. 'Gareth, leave your barnet alone! Gareth! Stop touching your hair!'
"It was the same pattern every morning: Gareth would tumble and stay there, and they'd all go running over. In the end I told them just to leave him alone.
"Don't worry,' I said, 'he'll be fine in two minutes. If it is anything urgent we'll soon know'. That's what they did and, as predicted, Gareth got up, got on with it and got better and better."
Bale spent most of his time under Redknapp on the left wing and really came to the attention of a European audience with his performances against Inter Milan in the UEFA Champions League.
Redknapp recalled: "I predicted he would be our Cristiano Ronaldo. And that's just what he was. I don't think I have ever seen one player terrify a team so completely as Bale did Inter Milan.
"I felt sorry for their Brazilian right-back. It was embarrassing. By the end of it the fans were singing, 'Taxi for Maicon,' and I don't think his career has ever recovered."
While Bale enjoyed the finest season of his career last term under Andre Villas-Boas after being given more freedom in a central role, Redknapp remembers when he first gave the player the opportunity to play in such a position.
He said: "I had talked with our coaches for a number of months about using Gareth this way because teams were crowding him out on the left flank, putting so much traffic in his way that it was just getting harder and harder.
"I remember the new plan coming together against Norwich City on December 27, 2011. He was magnificent, scoring twice as we won 2-0.
"Unfortunately, Gareth's switch then coincided with a few dicky results for us and a few people, looking for easy answers, put two and two together and ran out of fingers.
"Of course, a year later when he was scoring for fun in that position in Andre Villas-Boas' team, it was hailed as a genius move."
Bale sealed a record-breaking move from Spurs to Real Madrid this summer and Redknapp is interested to see how he will cope with the extra scrutiny of playing for one of the world's most high-profile clubs, admitting that his confidence could suffer if his partnership with Ronaldo does not flourish.
Queens Park Rangers manager Redknapp explained: "His biggest test will be to step out of the shadow of Cristiano Ronaldo with confidence. That won't be easy.
"Ronaldo is a huge star at Madrid and will probably want to take nine out of 10 free-kicks - at least. Gareth will have to assert himself and that will require a strong mind.
"It is a tricky balancing act. He will have to be ready for the matches when he goes it alone, has a shot, misses and Ronaldo starts throwing his arms up in the air.
"His relationship with Ronaldo is the key to it all, because if the football is going well then all the added stresses are a minor irritation and nothing more.
"If Ronaldo feels threatened by Gareth's arrival, Madrid could be a lonely place so he will need to lean a lot on Ancelotti, who speaks good English, and Paul Clement, Carlo's assistant, who is English.
"Madrid must guard against Gareth falling into the role of support act. He had a little trouble adjusting to the bigger environment of Tottenham after leaving Southampton and this is 10 times as great as that move.
"If I have a worry it is that I remember the days when Gareth's confidence was draining fast at Spurs and there were genuine fears he might not make it. He wasn't the strongest of characters back then and he cannot be allowed to fall into that same negative state of mind.
"The positive is that Gareth has grown a lot since his earliest days at White Hart Lane. His performances improved but so did his attitude.
"He has to take that maturity to Madrid, though, or it will be hard."