Spurs have led the chase for the final Champions League spot from the off this term, impressing under the stewardship of former Chelsea boss Andre Villas-Boas.
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"I rate the current Spurs team very highly," King told BBC School Reporters. "I think we've got a young and ambitious manager who's great and is going to do well for the club.
"I think we've got a great group of players at a good age where they're improving all the time and reaching their peak."The way the team are progressing at the minute, hopefully in the next year or two they will be really challenging for the Premier League.
"It's a big club and you've got to make sure it's not just a one-off, you've got to keep doing it. Hopefully we can qualify this season and continue doing that for the future."
The former England international also underlined the importance of Tottenham moving on from their White Hart Lane home in order to better its 36,000-seat capacity.
"We have to keep moving with the times," he continued.
"Ours is a great stadium and I'll be sad to see it go but we've got so many fans all over the world and it would be nice for more fans to come and watch the team play.
"The new stadium will be next door, here on White Hart Lane, which is important."