Pochettino spoke of his hope on Monday that Kane could be back for Wednesday's match at Wembley, but stressed it would be down to the player whether he felt up to playing.
Kane has scored 13 goals in all competitions this season and it seems optimism is growing that he could make a welcome return to the starting XI for the Madrid clash.
"We are really confident," Pochettino told a news conference.
"It may be possible but I don't want to say 100 per cent as we have one more day.
"He trained today but it is important we make the right decision."
Despite the undoubted importance of Kane, whose absence was keenly felt at Old Trafford at the weekend, Pochettino does not believe the striker's presence will make or break Spurs' chances of improving on their impressive 1-1 draw at the Santiago Bernabeu a fortnight ago.
"Of course it's a game where you have to be brave," he added. "If you are not, you start losing.
"For me, one or another starting selection is not important. It's more about our squad, not to pick one or another.
"Of course we are brave in the way we are going to play.
"We must play free and enjoy the game. If you show fear it's difficult to show your quality."
One man Pochettino will definitely have at his disposal is Kane's England colleague Dele Alli, who has been suspended for the opening three matches of Spurs' European campaign thanks to a red card in last season's Europa League.
"It's true that Dele Alli is so important to us but we are in a good position in the Champions League without him," Pochettino said.
"That shows a strong mentality.
"Of course he's going to help us now. I think he needs to enjoy playing football.
"He's a character, a winner and he needs to show his personality on the pitch as he did against United. That is his character.
"He has a good chance to play if I select him and we have one more player to help us achieve what we want, to go to the next stage of the Champions League."