The 21-year-old striker has scored 11 times in all competitions this term, having previously been linked with a loan move to Palace during the close-season.
"Always my idea was to keep Harry Kane, because we believe in him and his potential to play for Tottenham," said Pochettino, who arrived at White Hart Lane in May.
"He has shown we were right in our decision to keep him. He doesn't feel any pressure on him and that is important because he is a player who feels the club.
"He has come through the academy and always identifies our values. He is English, he shows passion and is in good condition - he is a very important player for us."
Pochettino revealed Emmanuel Adebayor will again be missing this weekend after picking up a virus, following on from hamstring and back problems.
"He still feels weak and maybe for the next few weeks is unable to help the team," added the head coach.
"But everyone in the squad is part of the plans for the future.
"It is normal for the media to speculate over players at the club but I can't comment because I don't read anything. I have a very good relationship with Emmanuel."
Pochettino revealed Kyle Naughton and Vlad Chiriches are also doubtful and has urged Tottenham to stay focused ahead of the clash with Palace on Saturday.
Following two tough tests against Everton and Chelsea, the Spurs boss warned his players not to let their guard down.
He told Spurs TV: "The Premier League is very competitive and we need to be careful against all teams.
"Each game is different, as it is true that Crystal Palace lost against Aston Villa but won against Liverpool.
"They have very good players and are a very tough team, but we need to focus on our game and it doesn't matter what Crystal Palace do.
"It is important to show respect for the opponent but we need to focus on our game.
"It is important to keep the same feeling and try to play in the same way as we did against Everton. This is our challenge to build up and move forward."