Only goal difference is keeping Spurs out of the top four after they extended their winning run to seven victories in eight games with Sunday's 3-1 triumph over Fulham. Manchester City and United are positioned first and second in the table, but King insists Tottenham are ready to restore pride in the capital.
"I hope we can become the biggest challenger to the Manchester teams," he said.
"We're still learning, we're still taking one game at a time, but at the moment we feel we can win every game we go into."
King believes Spurs' success in surviving a second-half onslaught at Craven Cottage proves they now possess the stomach for a fight, a quality that has been missing in previous years.
"We didn't play well against Fulham in the second half and we got lucky at times, our goalkeeper Brad Friedel had to pull off a few good saves for us," he said.
"But when that's happening you have to dig deep, and we did that.
"What they say about the old Spurs sides is that when it gets tough they weren't able to stick it out. This is a different team. We're managing to grind out results.
"That's seven wins in eight games. You have to be a good side to do that, and you have to do all forms of the game. You have to defend and score goals, and we're doing that.
"We're confident at the moment, we feel we've got a really good team. Everyone is maturing. We've got players that are reaching ages now when they understand the game a bit more, and what's expected of them."
Source: PA
Source: PA