Andre Villas-Boas's side currently sit third in the table, five points behind second-placed City.
King has admitted that he is impressed with the job Villas-Boas has done at White Hart Lane so far.
"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," Soccerway quotes King as saying.
"We beat Manchester United away for the first time since 1989 and he has shown that, tactically, he can compete with the big managers.
"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."
Spurs host North London rivals Arsenal in the Premier League on Sunday afternoon.