Crystal Palace boss Neil Warnock claimed on Thursday he tried to sign Kane on loan before the start of the campaign but that Spurs were keen to keep the striker for their Europa League fixtures.
Kane has scored 11 goals in all competitions for Spurs this season and his impressive performances have seen him start all of Tottenham's last four Premier League matches.
"It is the first time I have heard this information," Pochettino said in response to Warnock's comments, which came 48 hours before the sides meet at White Hart Lane on Saturday.
"I have never known it was possible. Our first idea was to keep Harry Kane and give him chances to play.
"My idea was to keep Harry because we believe in him and his potential to play for Tottenham.
"He has since shown we were right in our decision to keep him.
"At the moment Harry is not feeling any pressure. It is important that he is a player who feels the club, he came through the academy and he knows our values.
"He is English, he shows passion and is in very good condition — he is a very important player for us."
Kane's emergence has led to questions over the future of Emmanuel Adebayor, but Pochettino says the striker remains in his plans, although he will be absent this weekend as he continues to be troubled by a virus.
"My relationship with Emmanuel is very good, I was a player and I understand my players," Pochettino added.
"After the international break he came back with a back problem and after that he got a virus.
"I spoke with him today at training and he is not ready to play, he still felt weak — maybe in the next few games he will be ready to help the team.
"All the players in the squad are in my plans for the future. It is normal for there to be a lot speculation in the media around the players and the club but for me I don't comment on that."
Pochettino was coy on speculation playmaker Christian Eriksen has signed a new deal with the north Londoners, saying: "Eriksen new contract? Maybe. It's speculation though. I have no information. I'm happy with him. He's young and will improve."