On Sunday (22 October), two goals from Kane and one apiece from Son Heung-Min and Dele Alli saw Spurs demolish Liverpool 4-1, a result which moved them up to second in the Premier League table alongside Manchester United , five points behind Manchester City.
"We've been title contenders the last two years now and we have been very close," Kane told Sky Sports at the FIFA Best Football Awards on Monday.
"Manchester City are out in the front at the minute but there is a long way to go."
Spurs face United at Old Trafford, a ground where they have failed to score in their last three league visits, in the early kick off on Saturday (28 October) and Kane believes his side can put down a marker.
"We are a team that not many people talk about at the start, but we are there and we will be there, hopefully, for the rest of the season and then we will see what happens," he added.
Under Mauricio Pochettino, Tottenham have developed from a top four contender into a title challenger, finishing fifth, third and second respectively over the last three campaigns and last season's runners-up spot was Spurs' best league finish since they finished second in the league in 1962-63.
Kane, who has scored 15 goals in all competitions since the beginning of September, has played a pivotal role in his side's growth, after developing into arguably the best striker in the Premier League. The 24-year-old's exploits have seen him being linked with a move to United or Real Madrid.
The England striker has scored 38 goals in 33 appearances for Spurs over the course of the calendar year, a better record than that of Cristiano Ronaldo during the same period, but he admitted he still has work to do to reach the level of the Portuguese and Lionel Messi.
"[I have to perform] on a consistent basis and on a big stage for example in the Champions League and in World Cups and by winning trophies as well," he explained.
"They have set the standard for everyone but I've just got to keep improving, keep getting better and see what happens."
Last week, Rio Ferdinand warned Spurs could run the risk of losing Kane, should chairman Daniel Levy not be prepared to break the club's rigid wage structure to hand the striker a more lucrative deal than the £100,000-a-week (€112,020) he signed in December last year.
"Pay the man the money," Ferdinand told BT Sport.
"You gotta keep him at the club. If I'm Harry Kane then the chairman [...] his phone number is the most dialled number on my phone, because I'm telling them there needs to be parity within the league."