The 21-year-old has recently been linked with a move to Spanish giants Real Madrid.
Speaking in his column in the The Sun, Redknapp said: “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.
“Jose certainly knows a player when he sees one. But one thing is for sure. I am not letting Gareth go anywhere.
“Tottenham is a team on the up and we are building something at White Hart Lane.
“Mourinho can enjoy watching Gareth all he likes but he will be going nowhere.”
Redknapp has likened the Welsh youngster to Chelsea star Ashley Cole.
“I do not make comparisons lightly but he and Ashley Cole are quite similar and that can only be a massive compliment to Gareth,” said Redknapp.
“My left-back at Tottenham has come through an amazing 12 months and matured into one of the best players in his position in the world.
“Just over a year ago, he had this awful jinx hanging over him where he had not played in a winning Spurs team.
“Cole started out at Arsenal as a left-winger. Gareth was a left-winger as a lad too.
“Now, I would say he and Ashley Cole are two of a kind in this country and the two best left-backs in England.”
He added: “The main difference between him and Ashley Cole is that he is Welsh – more’s the pity.
“I would go so far as to say that Gareth is the best player to come out of Wales since Ryan Giggs. As an Englishman, I am highly disappointed he is Welsh.”