Spurs, who have not won the title since 1961, are currently five points behind league leaders Manchester City.
"We are in a great position at the moment and have probably surprised a few people," King told talkSPORT. "At this stage of the season, to be talked about as still capable of winning the title is great for us.
"We are not getting too carried away at the moment, though. We are just getting our heads down and grinding out results.
"That is new to us and maybe people would expect us to fall away in the second half of the season but, as players, we believe in our ability and we believe we can keep getting results."
The North London club travel to Manchester City in the league on Sunday.