The England skipper has missed the club’s last five games after damaging an ankle during the 1-0 Premier League defeat by Manchester United on January 13.
He was ruled out by his club until March, but, after undergoing a spell of warm weather training, Kane is hoping to be back sooner than expected.
Speaking from the Super Bowl in Atlanta, he told Sky Sports News: “It’s going well. I went away for some warm weather training and we’re stepping it up.
“[We will] see next week how we go, start to get the balls out and just see how the ankle reacts. It’s going well so far, but we have just got to take our time with it and make sure we get it right.
“I never put a time on any of my injuries. It is just about how it feels. The ankle feels great at the moment, so as long as the swelling stays away and we can keep progressing, that would be great.”
Spurs have gone out of both domestic cup competitions in Kane’s absence, but have dragged themselves back into the title race with victories over Fulham, Watford and Newcastle, although watching from afar has proved difficult for the marksman.
He said: “I have been watching the last couple of games [Watford and Newcastle]. It’s been nerve-wracking watching them, but a couple of great wins.
“Obviously, I want to be there helping my team, but you have got to have a positive mindset. I am just trying to stay as positive as possible. Hopefully I will be back as soon as possible.”
Saturday’s hard-fought 1-0 win over the Magpies means Mauricio Pochettino’s side are four points adrift of leaders Liverpool and just two behind second-placed Manchester City, an impressive return against the backdrop of a crippling injury list, uncertainty over their new stadium and two successive transfer windows without signing anyone.
If people on the outside did not have faith, then Pochettino did.
“It’s about now praising the squad, the players, to be in the position we are in the Premier League, no one believed at the beginning of the season that this squad was capable of being there,” he said.
“Because of our belief, how hard we work, our mentality and everything, we are there.
“We don’t need to be in some position like today to convince ourselves about our capacity, our potential or possibility to win. We always believe in ourselves.
“We are there because we believe in ourselves. Then it’s if we are capable to fight until the end, to be close and fight until the end to go close to our opponent to be champions.
“We are there because we deserve to be there. We will see what happens in the future.”
It will take some effort for Tottenham to claim a maiden Premier League title given the fact they have lost six games so far.
But they have got themselves into the race by winning the rest, breaking the Premier League record for most consecutive games without a draw, now standing at 29 matches going back to last season.
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