The Wales international put pen to paper on Monday on a deal which ties him to Real until June 30, 2022, which expires just before he turns 33.
Bale has been regularly linked with a big-money move back to England, with Manchester United reportedly leading the chase for his services, but the former Tottenham player only has eyes for Real.
Asked if he could envisage ending his top-flight career at the Bernabeu even if it meant not playing in the Premier League again, Bale told a press conference: “Yeah, for sure. The reason I signed here for so long is because I’m very happy here.
“I feel more comfortable every year that I’m here as well. I’m improving my Spanish, my family’s more settled. I fully intend to see out my contract here.
“Obviously in the future, I don’t know when I’m going to retire, but I’m very happy here at the moment and for the next six years I’m not looking past that really.”
United have long been linked with a move for Bale, even before the Welshman left Spurs to join Real in 2013 for a then-world record fee of £85.3million.
As recently as last month there was speculation of a possible attempt by the Red Devils to sign the flying forward, but Bale himself insists he knows nothing about any transfer talk.
He said: “I couldn’t tell you if anyone’s been interested. Since I’ve been here I’ve been fully concentrated on playing for Real Madrid.
“I’m very happy here which shows why I’ve signed another six-year deal and we never really speak about these things. If (United) have (shown an interest) they have, I don’t know about it. The main thing for me is to concentrate on my football and everything else is dealt with behind the scenes.”
Bale was also giving nothing away about the finances behind his new contract.
Media reports have suggested the 27-year-old will now be earning in the region of £18million a year - £350,000 per week after tax - and is in the top three best-paid players in the world, along with Barcelona forward Lionel Messi and Real team-mate Cristiano Ronaldo.
When asked about his wages on Monday, Bale simply said: “That’s for me to know and no-one else to find out, sorry.”