Andre Villas-Boas' side are currently four points ahead of their fifth-placed local rivals in the Premier League and would take a big step towards Champions League qualification with a win at White Hart Lane.
But King believes Tottenham should be aiming higher than that, claiming that overturning a five-point deficit and catching second-placed City is a genuine possibility.
“It’s Andre Villas-Boas’s first season in charge but they’re already showing great signs of being able to compete at the very top level,” King told reporters.
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“Confidence is high and there is no reason for the players to be looking behind them. They’re looking up, trying to keep this run of form going and to catch Manchester City.
“After another season or two with the manager, there is no reason why the club can’t be competing for the League title.
“The first step is the Champions League and when you get there, you can attract the calibre of player you need and push for the title. We lost some players last season but we’ve added others and we’re just as strong. The club are confident and the team are going from strength to strength.
“The chairman [Daniel Levy] has been trying to build strong sides for years. There have been difficult situations, for example when Dimitar Berbatov and Luka Modric left [in 2008 and 2012 respectively] but we want to build a team who can compete at the highest level of the Premier League.”
The 32-year-old also insisted that there will be no repeat of last season's slip-up which saw Spurs throw away a 10-point lead to allow the Gunners to finish above them.
“The players are aware of the situation last year and the lead we had,” he said. “You always want to do better and that’s the way the players feel about this game. They’re looking strong and there are no signs of letting up.
“I miss the atmosphere, which was the best I’ve experienced, but it’s for other players to taste.”