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.”
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.”
Spurs 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.