Kane, who has scored 13 goals in 12 appearances in all competitions for Spurs this season, was clutching his hamstring when he was substituted in the final minutes of their 4-1 win over Liverpool last weekend.
Speaking at a pre-match news conference on Friday, manager Mauricio Pochettino said the England forward could return for the Champions League group-stage match against Real Madrid at Wembley on Wednesday.
"The injury is very small but we cannot take a risk for tomorrow," he said. "We'll see after for Wednesday against Real Madrid. But tomorrow, it is impossible.
"Always you want to have all the players available, so this is a problem. But, like always, we believe in the collective, in the squad and during the season sometimes these things happen. We have to trust in other players."
Tottenham are currently third in the league, trailing second-placed Manchester United on goal difference and five points behind leaders Manchester City.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
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