Former Spurs boss Tim Sherwood had told Sky Sports News on Wednesday that the England striker could only show "so much loyalty" to his club should they fail to get their hands on trophies.
The 48-year-old said: "The only way they can keep him is to win something this year. That something might not be the Carabao Cup, it might have to be the league or the FA Cup."
Ahead of Saturday's lunchtime trip to West Ham United, Tottenham boss Pochettino responded by telling reporters: "Harry is one of the best strikers in the world and many people are talking about him.
"Some people are also saying we must win trophies for Harry to stay with us but it's already been made very clear. He's one of our best strikers, Harry is our player, he loves Tottenham, he's staying here and he's looking forward to staying here for a long time.
"Tim (Sherwood) has the right to speak about Tottenham and Harry. But that is a question more for Harry and what he's going to do. The answer is Harry has the power and decision to say what he wants to do in the future."
The last trophy won by Spurs was the EFL Cup in the 2007-08 season.