Spurs moved back into the top four with a 2-0 win over Blackburn on Sunday, but Bale has hinted that he would consider leaving White Hart Lane in the summer if they fail to qualify for Europe's elite competition.
But Redknapp insists Bale, who has been linked with Spanish giants Barcelona, is not ready to leave the Premier League.
"He has got a long contract at the club, I don't think he will be going anywhere, he isn't going to find too many better clubs than Tottenham," Redknapp said
"I don't think he is a boy to go abroad at the moment. The first opportunity he gets he goes home to his family in Wales so I don't think he is a boy who would be suited to go abroad at this stage of his career.
"I think this is a great club for him to be at and you can't be letting Gareth Bale go, he is the future of the club."
Redknapp added: "I think the chairman would want to keep him and you need to keep your best players. We need to strengthen the squad in the summer there is no doubt about that, two or three quality players if you want to push on next year and mount a challenge."