The Blues' desperate start to the season has seen them win just three games and lose seven, with many believing Jose Mourinho will struggle to guide his underperforming team to a top-four spot.
As a result of their poor form, Kane and company have taken advantage and look to be genuine contenders for a place in the Champions League having gone unbeaten in the league so far.
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When asked about Chelsea's prospects, according to the Express, he said: "Obviously they're not playing very well at the moment but I wouldn't write them off.
"They were champions last year for a reason. 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."
Despite a dismal season thus far, it appears Mourinho's job at Stamford Bridge is safe for the time being, with several of his players gearing up for another international break.
The Portuguese may use this time to shake up his squad, with rumours suggesting he's ready to axe some of his underperforming stars.
The 52-year-old was present at Chelsea's Cobham training ground on Sunday, as he watched the Under-21's beat Liverpool 4-0. Ruben Loftus-Cheek impressed after scoring from kick off - and Mourinho may turn to him amidst Nemanja Matic and Cesc Fabregas' poor form.
It's likely he will also look to spend big in January, should he still be in charge, of course.
Chelsea will resume their campaign against Norwich at home Saturday week, with the Blues desperate for their first win since mid-October.