Second-placed Spurs trail their London rivals by nine points in the Premier League.
Antonio Conte’s side saw off Arsenal at Stamford Bridge on Saturday to all but rule Tottenham’s neighbours out of the race.
Kane’s penalty in Spurs' 1-0 win over Middlesbrough kept them just about in touching distance of Chelsea.
To celebrate the victory, on Monday 6th February, England striker Harry Kane partnered with Lucozade Sport to host an exclusive training session with over 140 fans in support of Lucozade Sport’s Made to Move campaign.
Tottenham's Harry Kane says they can't control what Chelsea do
We can’t control what Chelsea do
While Tottenham face Liverpool at Anfield on Saturday (5.30pm), Chelsea travel to Burnley the following day (1.30pm), meaning Kane and his team-mates can put some early pressure on the league leaders.
The 23-year-old is fully focused on Spurs’ next task, as Kane accepts he will just have to hope the Blues slip up.
“We can’t control what Chelsea do,” Kane told Express Sport. “All we can do is concentrate on our games and winning as many as we can from now until the end of the season.
“Our aim now is to win trophies and we believe we are good enough to challenge for the Premier League title.”
Tottenham star Harry Kane hosted a training session with fans for Lucozade Sport on Monday in London
While Kane is battling at Spurs for title glory, he also has a personal agenda for the rest of the season.
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The England forward is on 14 Premier League goals, and sits two behind top scorer Romelu Lukaku in the race for the Golden Boot.
Everton’s hitman netted four times against Bournemouth on Saturday, while Arsenal’s Alexis Sanchez, Chelsea’s Diego Costa and Manchester United’s Zlatan Ibrahimovic each have 15.
But even though he is in the running for the personal accolade, Harry Kane insists Spurs’ aims are more important.
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He added: “Am I targeting the Golden Boot?
“Every striker wants to score goals but winning trophies with the team is my main ambition.”
Tottenham are still battling in three competitions with Premier League, Europa League and FA Cup glory still possible.
At least one trophy would be an ideal way for the team, the fans and the club as a whole to bid farewell to White Hart Lane this summer.
England hitman Harry Kane was involved in the shooting drill at Lucozade Sport's training event
And under the guidance of Mauricio Pochettino, Kane believes Spurs will continue to grow.
“The new stadium is such an exciting prospect for us; it’s all part of the journey,” Kane said.
“It will be sad to leave White Hart Lane but the new ground is a great step for this club.
“We are going in the right direction, with one of the best managers in the world, a world-class squad and training centre and soon to have a world class stadium.”
Lucozade Sport’s Made to Move campaign is aiming to get 1 million people moving more by 2020. Find out more at www.lucozadesport.com/madetomove