Bale has reportedly been earmarked by Madrid as a saleable asset as they look to raise funds to a move on Monaco prodigy Kylian Mbappe, who could cost the European champions an estimated €180 million.
After the winger helped Madrid overcome United 2-1 in the UEFA Super Cup on Tuesday, United boss Jose Mourinho said it was "game over" in their pursuit of the former Tottenham man. Florentino Perez has also insisted that last season's double winners want to hold onto the 28-year-old .
Having made just 27 appearances in yet another injury-punctuated season at the Santiago Bernabeu, Bale now hopes that he can work his way back into Zinedine Zidane's plans.
"For me, I just want to concentrate now on getting fit, getting ready for the new season and playing as well as I can, ultimately," he said.
Asked if he had told Real Madrid of a desire to stay, the Wales star laughed: "There's been no need for anything.
"Everything's gone on as normal, like it has every year. There's been the normal speculation like there is every year.
"Obviously it's a little bit more hyped up because we were playing Man United today. So it's one of those things.
"I'm focused on my football and getting into shape. I'm happy, I play football, I win trophies ... I just want to concentrate on being ready for the new season, and playing the best I can.
"The club have not told me anything about my future but we have talked and are happy with everything."
Madrid are yet to sign a replacement for Alvaro Morata, after selling him to Chelsea, with Mbappe's name often placed alongside the likes of Eden Hazard and Ousmane Dembele as potential attacking purchases.
Bale does not feel threatened by the speculation, however, accepting it as part and parcel of playing for one of Europe's biggest clubs.
"I feel like I'm happy to fight for my place," he said. "We're all fighting for our places anyway - it's nothing new in football, it happens at every club and you carry on as usual."