Bale only moved to Real from Tottenham in September 2013 but, midway through his second La Liga campaign, the British media is widely convinced the Welsh winger is a major target of United manager Louis van Gaal.
But speaking on Spanish radio station Cadena SER, Bale refuted those rumours, indicating the opportunity to regularly win silverware makes him keen to see out his contract that runs until June 2019.
"For me, no," Bale said.
"I did an interview recently and I said I'm happy here, I've got several years left on my contract and I'm having a good time.
"We're winning trophies and I want to stay here."
Bale has won the UEFA Champions League, Club World Cup, Copa del Rey and UEFA Super Cup since signing Real - reportedly for a world-record fee of €94million.
That fee, plus claims in the Spanish media that Bale is a "ball-hog", has been the focus of a perceived rift between the 25-year-old and team-mate Cristiano Ronaldo.
Bale was criticised for shooting himself instead of passing to Ronaldo during Real's 2-1 loss at Valencia on January 4 and their 3-0 triumph over Espanyol six days later but the Welshman was unmoved.
"People [in the media] have their own opinions and that's how they make their living," he said.
"It's their work, they get paid to do it.
"I think that when I'm playing I set goals up and I score them too. I play football my way."
Bale added he has not discussed his on-field decision making with Ronaldo:
"No, we didn't speak about it afterwards. It happens all the time in football.
"It's something that just gets left on the pitch. Nobody talks about it afterwards."
The former Tottenham flyer has scored 14 goals in all competitions this season, while setting up another seven, with all but one finished off by Ronaldo.
Bale also denied claims he is struggling with his back or a hernia: "No, I don't have anything. It's not true."
