The Premier League's joint leading scorer was forced off the field during the second half of his side's 4-1 win at Bournemouth on Sunday following a collision with Cherries keeper Asmir Begovic that left his right ankle injured.
The 24-year-old underwent scans on Monday and while the full results have yet to be announced, The Mirror claims that Spurs are fearful of a six-week layoff.
Kane has injured his ankle twice previously over the last 18 months, first missing seven weeks in September 2016 before spending a further three weeks on the treatment table a year ago.
Should Spurs' fears prove correct, the striker would miss the FA Cup quarter-final, four Premier League fixtures and England's two international friendlies later this month.
Kane would then be left to play in just a handful of Premier League games before the end of the season ahead of the Three Lions' trip to Russia for the World Cup in June.