The Welshman, 25, had been linked with a move to Old Trafford, with goalkeeper David De Gea going the other way.
"I can't see myself at Manchester United," Bale told radio station Cadena SER. "I am enjoying myself and we are winning trophies. I want to continue doing this at Real Madrid."
Bale joined Real for an £85m world record fee in September 2013 and won the Champions League last season.
The former Tottenham player has been criticised by some sections of the Madrid supporters recently and was booed after failing to pass to Cristiano Ronaldo in a 3-0 win against Espanyol.
Ballon d'Or winner Ronaldo, who showed his frustration at being denied a tap-in at the time, later urged the club's fans to back his team-mate.
Bale said: "I feel the support of the Bernabeu. I am going to continue working to show what I am capable of doing on the pitch and so as to win more trophies.
"I don't think I'm greedy. On the pitch I make assists and score goals. I play the game how I like to play and the press can say what they want."
On his relationship with Ronaldo, the Wales international, who revealed he used to be an Arsenal fan, added: "There is no rivalry between us."
Bale, who has also won the Copa del Rey with Madrid, has scored 36 goals and provided 26 assists in his 72 matches for Real.
Real Madrid forward Gareth Bale has ruled out a move to Manchester United.