Mauricio Pochettino's side are four points behind leaders Chelsea at the top of the table, having amassed a club record of 74 points this season.
A victory over Arsenal in Sunday's north London derby will guarantee that Spurs will finish above the Gunners in the top flight for the first time since the 1994-95 season and inflict a damaging blow on their rivals' hopes of a top-four finish.
Kane, however, says their priority is on closing the gap to Chelsea and keeping their title hopes intact.
"For the fans, it would be great to finish above Arsenal and actually do it by winning against them but, from our point of view, we've got bigger things to look forward to," he said.
"We've got to try and win that game to keep the pressure on Chelsea as much as we can."
Spurs battled to a 1-0 victory at Crystal Palace in their last outing to stretch their run of top-flight wins to eight in a row.
Kane believes their victory at Selhurst Park, which came courtesy of Christian Eriksen's late strike from distance, underlines the impact Mauricio Pochettino has had since being named manager in 2014.
"Since the gaffer has been here, he's changed everything and he's been fantastic. You see the belief in the squad; you see the way we play," said the England striker.
"Sometimes, we win 4-0 and we play fantastically and then there are nights like last Wednesday at Crystal Palace when we have to dig deep and get a 1-0 win. We did that and it shows we can do both sides of the game.
"The gaffer has installed his philosophy with the way we play – the pressing and getting the ball down – but he's also installed that steel in us; that we've just got to find a way to win. He's a very passionate manager and that bleeds into the rest of the team."