Kane, who has scored 13 goals in 12 appearances in all competitions for Spurs this season, missed defeats by West Ham United and Manchester United after suffering a minor hamstring strain.
“We’re very confident (he will play) - he’s on the list. We have one more day to assess him but maybe it’s possible he can play tomorrow,” manager Mauricio Pochettino told a news conference on Tuesday.
”I don’t want to say 100 percent because we have one more day. Today and yesterday was good at training. Now it’s with medical staff to take the right decision.
“He was training with group and was good - at same level as team. We’ll take the best decision for him, first of all, and then for the team.”
Winger Erik Lamela, who has not played for a year due to hip problems, also took part in the training drills. Midfielder Victor Wanyama was Spurs’ only absentee but he will resume training later this week.
Spurs will be also boosted by the return of Dele Alli, who was suspended for the opening three matches of their European campaign.
“He has a good opportunity tomorrow to play if I decide to put him in the starting XI, and make his Champions League debut (this season),” Pochettino said.
“I‘m happy because we have one player more to help the team what we want to achieve, to reach the next stage of the Champions League.”
Tottenham and Real are level on seven points at the top of Group H after a 1-1 draw in Madrid this month.