The England and Spurs captain has been sidelined since suffering a torn hamstring during a Premier League defeat at Southampton on New Year's Day.
Kane has made swift progress with his rehabilitation and would be back in full training next month if the season was not on hold due to the coronavirus pandemic.
He told Spurs TV: "I'm not too far away – I'd normally hope to be back with the team in two or three weeks’ time.
"I'm at a good stage, pretty much doing everything, now it’s about building up my fitness.
"From a rehab and personal point of view, I’m in a good place, I'm doing really well.
"I’m at a good stage now and just working hard, doing a lot of recovery, a lot of rehab and just waiting to see what happens to the season.
"Other than that, my family is well. Obviously everyone is thinking about coronavirus at the moment and it’s a time to be together, to stay safe and hopefully everything will be alright."
The Premier League season has been suspended until at least April 30, with the campaign extended 'indefinitely' as the United Kingdom begins a lockdown.
Kane added: "It's such a strange situation, no-one has been in this situation before. Like anything, you have to take the positives out of it and do what you can.
"So far, me and the family are well, and I'll continue to work hard, work in the gym, work from home and do what I can. We'll just have to wait and see.
"I'm taking it all as it comes but for the time being, I'm in a good place, happy where I'm at and let's see what happens."
Prior to his injury setback, Kane had scored 11 goals in 20 league appearances this season.