Kane has scored 13 goals in 12 games for Spurs this season but missed Saturday’s 1-0 defeat by Manchester United with a hamstring problem.
He took part in training on Tuesday and could play at Wembley.
“He’s on the list. Maybe it’s possible for him to play but I don’t want to say 100%,” said Pochettino.
Spurs would qualify for the knockout stages of the Champions League with a win – as would their opponents Real.
The hosts are top of Champions League Group H, above the defending champions on goal difference. Both sides are six points clear of Borussia Dortmund and Apoel Nicosia.
Spurs winger Erik Lamela is available after just over a year out with a hip problem, but midfielder Victor Wanyama is still out with a knee problem.
Real forward Gareth Bale will miss the game against his old club after failing to recover from a calf injury. First-choice keeper Keylor Navas and centre-back Raphael Varane remain injured.
Real manager Zinedine Zidane is facing criticism in Spain after a shock 2-1 defeat at La Liga minnows Girona on Sunday.
They are eight points behind leaders Barcelona after losing two and drawing two of their opening 10 games and Zidane said: “Perhaps some people might think that after a defeat we are down in the dumps but that’s not the case.”
“We all know how football works, sometimes you are going to lose matches and it’s obviously frustrating.
“After a defeat people aren’t happy but in some ways I like this. I like that we have a big game coming up. I feel I work my best in these situations.”
The Reds have lost one of their last seven games in all competitions and top their Champions League group on goal difference ahead of Spartak Moscow.
In their previous game in the competition, they thrashed Wednesday’s opponents Maribor 7-0 away from home.
“We have had injuries and I think we are waiting for it to click,” Milner said ahead of the game.
The former Valencia player, 31, who has been at City since 2010, has 18 months left on his current deal.
Silva helped City win the Premier League in 2012 and 2014, the League Cup in 2014 and 2016, and the 2011 FA Cup.
“I pray every night to win the Champions League with City,” said Silva.