Spurs, who have won their last eight games in all competitions, face league leaders Chelsea in Saturday’s FA Cup semi-final at Wembley.
At an individual level Kane, the league’s top scorer last season, trails Belgium international Romelu Lukaku of Everton by four goals with six Premier League games to play.
“As a striker you want to be top scorer in the league, no doubt about it,” Kane said.
“I left a couple out there I probably should have scored, Lukaku has been doing well and it’s a good competition but the main thing is we’re winning games.
“I’ve a little eye on the run-in and if I can get a few more, we’ll see what happens,” Kane added.
The 23-year-old England international became the first Spurs player since Jimmy Greaves in 1969 to hit 20 goals in three successive top-flight seasons after netting in the club’s 4-0 win over Bournemouth last weekend.
After the FA Cup semi-final, Spurs will shift focus to the league, where they trail Chelsea by four points, ahead of a trip across London to Crystal Palace on April 26.
Spurs last won the English league title back in 1961.
Kane told Tottenham’s website that Spurs must focus on maintaining their momentum heading into a difficult run of fixtures, which includes home games against fifth-placed Manchester United and North London rivals Arsenal.
“We’ve some tough games coming up — (Crystal) Palace away, Leicester away, Arsenal and (Manchester) United here but we’re feeling good, we’re feeling confident,” he said.
“Every game we go into we feel like we’re going to score goals and defensively we’re keeping clean sheets, so that’s what we’ve got to try to maintain until the end of the season.”
Meanwhile, John Terry says the decision to leave Chelsea was the “toughest of my life”, but revealed he wants to play regular football again.
Terry and the Blues this week announced the 36-year-old will bring the curtain down on his illustrious Stamford Bridge career at the end of the season.
The club captain has won 14 major honours and made 713 appearances since his first-team debut in 1998. But Terry has been a bit-part player for the Blues this season, featuring in just five Premier League games for Antonio Conte’s table toppers, although he could feature against Spurs.
Writing on Instagram, the former England skipper said: “It’s with overwhelming emotion that earlier this week the club and I announced this will be my last season as a Chelsea player.
“This has been the toughest decision of my life for me and my family, but I always envisaged leaving on the right terms, in the right way and at the right time — and that is now.
“I feel I still have regular football in me but understand that opportunities here at Chelsea will be limited. It is therefore time for a new challenge.”
Terry made no mention of his next destination, with China or the United States possible options as well as potentially staying in England with the likes of Bournemouth, who were linked with the defender in January.
However, Terry, who has made enough appearances to receiver another Premier League winners’ medal this term should Chelsea land the title, did reiterate his desire to return to the Bridge in another role somewhere along the line.
“I look forward to returning to this great club in some capacity in the future,” he added.
“I want to stress that the journey is not yet over. There is a long way to go and we are committed to ending this campaign on a high.
“I am fully focused on helping the team and manager in every way I can until the and of the season.”