Despite playing a significant role in Real winning their celebrated 10th European Cup and the King's Cup last season there has been talk of a move back to the Premier League for the Welshman.
He has been criticised by a section of the Real fans and the media for being greedy on the ball and failing to link up with his team mates.
It has led to rumours that he could be part of a deal where United goalkeeper David de Gea would move to Real.
"I can't see myself at Manchester United," Bale told Spanish radio. "In an interview recently I was asked if I was happy in Madrid and I said that I was very happy here.
"I have a long contract still to go, I am enjoying myself and we are winning trophies. I want to continue doing this at Real Madrid."
Bale was singled out after Real's defeat against Valencia in their first game back following the Christmas break for not passing to Karim Benzema who was well positioned to score, and he also whistled at the Bernabeu when Real played Espanyol.
"(Against Valencia) I only remember running towards the goal, I wanted to score but it didn't go in," said Bale.
"If I had scored against Valencia and Espanyol then nobody would have said anything. I didn't see the pass and I don't think it was so easy but these things happen in football. They are part of the play.
"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."
Bale claimed he had a good relationship with Cristiano Ronaldo and that the criticism he had received would not affect his style of play.
"There is no rivalry between us. We have meetings to talk about tactics. Normally if there is a free-kick from the left then Cristiano takes it and on the right it would be me. We get on well," said Bale.
"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."
(Editing by Sudipto Ganguly)
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