The red hot striker has been dishing out plenty of humble pie in recent weeks.
His sixth goal in four matches against arch-rivals Arsenal on Sunday made a mockery of suggestions from some quarters that he is a one-season wonder.
His form, like that of his team, who haven't lost since the opening weekend, has steadily improved as Mauricio Pochettino's side have grown into the season.
The quiet rise of Tottenham
Spurs can justify that hype when they face West Ham and Chelsea in back-to-back London derbies after the international break.
'Trying not to think about the teams around us'
But Kane, who has joined up with Roy Hodgson's England squad for friendlies against Spain and France, has told Sky Sports he is not thinking about the huge double header, but admitted neither game daunts him.
"There's still a long way to go and we're not going to come out and say 'we're title contenders' but we've just got to keep doing what we're doing," he told Sky Sports.
"Obviously Chelsea are not playing very well at the moment but I wouldn't write them off. They were champions last year for a reason.
"Again, we've just got to concentrate on ourselves, try not to think about the teams around us.
"We're playing very well, we've got great belief and we've just got to keep trying to move up that table."
Tottenham take on West Ham on Sunday November 22 before they face beleaguered Chelsea a week later.
It is potentially crucial that both games are at White Hart Lane.
But if anything, it could well count against Spurs.
West Ham have been one of the best teams in the league away from home, beating Arsenal, Liverpool, Manchester City and Crystal Palace already.
And while they have suffered a huge blow with the news that star player Dimitri Payet is out for up to three months, the international break will give the likes of Alex Song and potentially Enner Valencia time to to recover.
Chelsea are struggling down in 16th place after their torrid start, but they may be grateful to get away from Stamford Bridge, where the pressure to win is becoming more acute by the week.