Bale won both the Player of the Year and Young Player of the Year following a superb last season for Andre Villas Boas' side.
The Welshman has been linked with a big money move away from White Hart Lane - with Real Madrid and Manchester United among rumoured suitors - but has always insisted he is happy in north London.
And King is convinced Bale will be part of Spurs' push for the Champions League next season.
"The season he had last year was a big part of our achievements, and he knows we'll be looking to do the same this season," he told Sky Sports News.
"I know Gareth's happy, he's come back in good spirits and I'm hoping he's going to have a good season again."
King also believes the 24-year-old will take the speculation over his future in his stride.
"I think you get used to it as a player," he added. "The kind of player he's grown to be, it's something that you have to deal with.
"He's a good lad, he's got a good head on his shoulders and he knows the main thing for him is just to concentrate on his football and the rest will take care of itself."