The 24-year-old is attracting serious interest from the Spanish giants after a remarkable season for Spurs.
One report today suggested Madrid have agreed to pay £105million for Bale - a deal which would smash the £80million world record fee they paid for Ronaldo when he joined them from Manchester United four years ago.
While there are clearly still hurdles to overcome, Redknapp, who worked with Bale for four years as Spurs boss, believes the winger would shine in Spain.
"He is behind Messi and Ronaldo in terms of being the best player in the world," Redknapp said.
"He is at a good club but the opportunity to play for Real Madrid does not come along too often. He has probably dreamt about that since he was a little boy.
"It seems they have offered fantastic money so it could happen, but I don't know. I wouldn't be sure.
"If he goes there, he will be a great success there. I am sure of that."
Redknapp, now manager at QPR, helped transform Bale into the player he is today.
Originally a left-back with Southampton, Redknapp pushed him further forward and was at the helm when he won the Professional Footballers Association Player of the Year award for the first time in 2011.
"He has been playing like that for three or four years," he said. "I think it was three years ago that he was Player of the Year the first time.
"He has been consistent over about a period of about four seasons so he has proved he can do it regularly, every year.
"He has got everything, he can do the whole lot - he can dribble, he can shoot with both feet, can head it, run all day, run at speed. There is nothing he can't do. He is an amazing player."