Kane captained England to the semi-finals of the World Cup in Russia this summer and is not due back in training until August 6, just five days before the start of the new campaign.
However, the 24-year-old is hoping to be fully fit and available for selection on August 11, when his side take on Newcastle United at St James' Park.
"I'm back on August 6 so obviously I'll keep training until then," Kane told Sky Sports News.
"But the Premier League starts on the 11th so we've got to make sure we are fit and ready to go. It's a quick break but that's part and parcel of the World Cup and things like that."
Spurs had nine players involved in the semi-finals of the World Cup - more than any other club.