However, Redknapp thinks that Spurs will be able to keep hold of the double PFA Player of the Year.
"Gareth won't want to leave, he's happy at Tottenham," Redknapp told talkSPORT. "He wants to be successful obviously but he's not someone I can see moving to Real Madrid at this stage in his life.
"His football is going great, he's PFA Footballer of the Year and loved in this country by football fans who know the game.
"He's very happy at Tottenham and I can see him staying for at least another year. Eventually he'll feel it's time to give it a go abroad, somewhere like Barcelona or Real Madrid, because he is capable of playing anywhere."
Redknapp also believes that his old side can mount a challenge to qualify for the Champions League next season, despite missing out on the final day.
"[Spurs] have got the nucleus of a good side," he said.
"It's the poorest Arsenal team I've seen in a few years but they still managed to scrape into fourth. I don't think they'll get away with that next year, they'll need to improve in the summer.
"Jan Vertonghen was top class last year and I can see them making the top four next season, but it's going to be tough."