Reports in Spain say that the flying Welsh winger has told Tottenham that he wants to leave and has agreed a six-year deal to join Real.
But King, a former England international who captained Spurs before retiring last year because of persistent injury, said: "There has been speculation all over the summer and I don't think it's going to stop till the window closes.
"As far as I'm aware Gareth is happy playing football at the club," King, now an ambassador for Spurs, said in Hong Kong, where the Londoners play Sunderland later Wednesday in the Barclays Asia Trophy.
"From the club's point of view we continue to try to work with Gareth and try to get the best out of him and hopefully he will be starting off the season with Spurs and finishing off the season the way he did [last term]."
King conceded that he had not spoken to the 24-year-old Bale over the summer, during which there has been almost daily speculation about his future.
"Not over the summer, no, but I have seen him here and he's in good spirits, looking forward to the season and, honestly, the news has been throughout the summer and will continue to be, so we just need to wait and see," said King.
"Speaking to him at the end of last season and from what I gather, he's in a good place at the moment and just keen to get fit and play some football and get the season started."
Bale, voted player of the year in England last season by his peers, is not expected to feature against Sunderland after picking up what manager Andre Villas-Boas described on Tuesday as a "knock" in training.
He may though return on Saturday, when Tottenham will play Manchester City or local side South China.
"Football is about speculation, especially when you've got the transfer window and you have players like that," said David Ginola, another ex-Spurs man.
"For us and for the people that really love Spurs, we'd love to see Gareth playing next season for Spurs," he said. "We'll see. We don't know at the moment what's going to be, we just hope that Gareth will stay for another season and give his best for Spurs."
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