The Wales forward, who has scored 10 league goals in 16 La Liga appearances for Real this season, is under contract with the Merengue outfit until June 2019.
Bale has been strongly linked in recent weeks with a move to Old Trafford with Manchester United reportedly keen to acquire his services.
However, Bale told Spanish radio station Cadena Ser: "I don't see myself at Manchester United.
"In a recent interview I was asked if I was not happy at Madrid but I told them that I am very happy here.
"I have many years left on my contract
I feel the support and love of the fans at the Bernabeu stadium
"I hope I can continue to work in order to prove what I'm capable of doing on the pitch and to win as many trophies as possible.
"The fans are amazing
I love when we play at home
"I'm having a good time, we are winning trophies and I want to continue to do this here, at Real Madrid."
Since joining Real from Tottenham in the summer of 2013, Bale has won the Champions League, the UEFA Super Cup, the FIFA Club World Cup and the Copa del Rey.
Real currently lead the league standings and are also alive in the Champions League, where they will face Schalke in the last 16 of the competition next month.
"The reason why we have won so many titles is because everyone rows in the same direction," the 25-year-old said
"During training, during games, everyone plays at a very high level."
Everything at Real is planned to detail, according to Bale.
"We have tactical meetings to see who takes free-kicks," he said
"If it's on the left, it's Cristiano Ronaldo, if it's on the right then it's me
It usually works well
"Now that Cristiano may not play, (likely to face a two-match suspension for being sent off in Saturday's game at Cordoba), I hope I can take the free-kicks in order to have the opportunity to score more goals."
Bale revealed his love for Real goes back to his childhood.
"I liked watching Real Madrid on TV," he said
"They always had the best players and played the best football.
"Whenever they played, it was always exciting
I was passionate about Real Madrid
"I really liked (Zinedine) Zidane and Ronaldo
To watch the two of them play together was incredible, just to see what they were able to do on the pitch
"That was the reason why I liked Madrid so much."
Source : PA