Kane scored the only goal in Spurs' win over Sunderland but left White Hart Lane on crutches after falling awkwardly in the second half.
Although there has been no official confirmation from Tottenham, the reports say the club now believe that Kane may have ligament damage, which would sideline him for six to eight weeks.
Tottenham are reportedly awaiting the results of a second scan on the striker's ankle to confirm how long he will be out.
If the damage turns out to be less than originally feared, Kane could miss as little as 10 days, and the club is confident that he does not have a grade-three tear that could rule him out for four months, the reports said.
The two-month time frame would rule Kane out for games against Manchester City, Leicester City and Arsenal.
Spurs signed Vincent Janssen from AZ Alkmaar this summer, but the forward is still looking for his first goal for the club in six appearances.