The former Southampton youth prodigy has been a key figure in the White Hart Lane club's resurgence under Redknapp, scoring in the North London side's memorable 4-1 triumph against Dutch champions Twente in the Champions League on Wednesday.
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Bale signed a new deal at Tottenham in May and, according to his current boss, the left-sided player will remain at the club despite managerial counterpart Mourinho being an admirer of his talents.
“I read in the papers the other day that Gareth's performances for Spurs have already caught the attention of other teams around the world - including Real Madrid and their manager, a certain Jose Mourinho,” Redknapp said in his column for The Sun.
"Jose certainly knows a player when he sees one. But one thing is for sure. I am not letting Gareth go anywhere."
Tottenham currently sit 8th in the Premier League table but Redknapp maintains his team are on the cusp of building success at the club, with Bale being a stalwart in Spurs' progression.
"Tottenham is a team on the up and we are building something at White Hart Lane,” he added.
"Mourinho can enjoy watching Gareth all he likes but he will be going nowhere."
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