The 23-year-old will not play against Bayer Leverkusen in the Champions League on Wednesday but could be in contention for when Tottenham take on Arsenal at the Emirates Stadium on Sunday.
If Kane does make the derby, he would also then be in contention to be selected by Gareth Southgate for England's fixtures later this month.
The Three Lions face Scotland in a World Cup qualifier at Wembley on November 11 before hosting a friendly against Spain on November 15.
Toby Alderweireld was also out training with Spurs on Tuesday but, unlike Kane, the defender was running on his own, separate from the rest of the group.
Alderweireld has missed Tottenham's last four matches with a leg injury.
Erik Lamela, who was ill and absent from the 1-1 draw against Leicester on Saturday, was back among the squad.