Harry Redknapp's men have stormed into the top three of the Barclays Premier League following a run of just one defeat from 19 matches.
Spurs head to the Etihad Stadium on Sunday five points behind leaders Manchester City following last weekend's 1-1 draw at home to Wolves.
Redknapp has urged his side to believe they can still have a say in the outcome of the championship, although admitted it will be a tough ask to overhaul both City and Manchester United - who visit White Hart Lane in March.
Centre-back King feels everything has to be kept in perspective.
"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."
He added: "We look at the league table and we can see we are in amongst it.
"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.
"We have lost just one in the last 19 and that is great form. If we keep it up then we are in with a chance."
Redknapp remains open to doing business in the January transfer window if he can find the right player.
Spurs, however, still have plenty of other options in reserve, with the likes of Heurelho Gomes, Niko Kranjcar, Roman Pavlyuchenko, Steven Pienaar and Jermain Defoe all desperate for more game time.
Mexico midfielder Giovani dos Santos is said to be a target for Spanish club Villarreal.
Defoe may have found himself down the pecking order behind on-loan Manchester City hitman Emmanuel Adebayor, but the England striker has played down suggestions he is keen to move on, with Liverpool a reported possible destination.
However, the 29-year-old, who has started just seven league games, concedes he is not happy being on the bench.
Defoe said on Sky Sports News: "At the end of the day it's not a case of me saying I want to go here, I'm not playing, I want to leave the club.
"I've been here six years - I've never said that once. I think the fans know that.
"It's just a case of me playing. I could understand if I was 19, 20 and I had time on my hands, but I'm 29 now and, like I've always said, all I want to do is play football. It's as simple as that."
Under the terms of the loan deal, Adebayor cannot play against his parent club on Sunday, which could see Defoe handed a rare start.
"As it stands I'm a Tottenham player and if I do play against Manchester City I'll be fully committed. I'm sure everyone knows that at the club," he said.
"The way we are playing is fantastic. The chances we're creating, the intensity we're playing at, the way we move the ball; it's just been great.
"It's a good time to be at the club. Everyone is enjoying it."
Spurs winger Gareth Bale was today named in UEFA.com users' team of the year, which was voted for by around 380,000 visitors to the governing body's website.
Five players from European champions Barcelona - Dani Alves, Gerard Pique, Xavi, Andres Iniesta and Lionel Messi - also made the line-up along with Real Madrid trio Iker Casillas, Marcelo and Cristiano Ronaldo, with Bayern Munich forward Arjen Robben and AC Milan centre-back Thiago Silva completing the team.
Wales international Bale said on www.tottenhamhotspur.com: "It's great to be recognised in such illustrious company, and the fact that it's voted for by fans across Europe makes it a special honour.
"But as I've said all along, I'm part of a team here at Spurs and any recognition I receive is down to my team-mates as much as anything that I do individually.
"The team has been playing really well and we've all played a part in that."
Tottenham announced a change to their commercial staff with the departure of Charlie Wijeratna, executive director with commercial responsibility.
Chairman Daniel Levy said: "I'd like to thank Charlie for his work since he's been with us. He has overseen the successful overhaul of the brand and the club's visual identity. We wish him the best of luck in the future."
Wijeratna added: "I've enjoyed my time at Spurs. It has been an exciting environment to work in and I am proud of the work I have done with my team to position the club for the next phase of its commercial development."