The Wales international has endured a tough second season in Spain as Real finished runners-up to Barcelona in La Liga and failed to retain the Champions League.
But despite speculation linking him with a return to the Premier League, he says he wants to remain at the Bernabeu and fight for more silverware.
“Of course, yes, I’m a Real Madrid player and I’ll carry on as normal,” he told The Sun when asked whether he would be at the club next season.
“I am enjoying it and hopefully I can continue to. I feel settled. I’m looking forward now to playing and winning more trophies.
“My goal is to keep improving, performing and to win as many titles as I can.”
The 25-year-old netted in last year’s Champions League final win over Atletico Madrid but missed out on the chance to lift the trophy again as Real were beaten by Juventus in the last four.
“We were devastated not to be in the final this year, but we will go again next year and try to win it like we always do,” said the Welshman.
“We will all be giving 110 per cent next season to win every trophy. Hopefully we can bring a few back.”
After a fantastic debut season in Spain, Bale came in for criticism during the 2014/15 campaign from fans and the press as he struggled for consistency.
But he insists it has been a “good experience” and is determined to get back to his best next year.
“Playing for Real Madrid is a learning curve for me. I’m still getting used to being at such a big club,” he said.
“It has been a great experience in good or bad times… Personally I have enjoyed it. I feel in part I have played well. Maybe I haven’t scored as many as I would have liked. It’s something for me to work on in the off season to get my finishing a bit better.
“The reason I came here was to get a different style of play under my belt and learn different things which I feel I have done and am doing.
“I still have my best years ahead of me – touch wood with injuries. I am looking forward to the future and to see what I can achieve.”