The England internationals have been linked with moves to Manchester United and Manchester City respectively in the English media this week, but the Argentinian dismissed reports the two would leave Spurs ahead of next season.
"There's a lot of rumours," said Pochettino, who himself has been linked with a move to Barcelona to replace the departing Luis Enrique. "I don't like to talk about rumours, that is another.
"During the season we hear many rumours for our players and myself too. We are not worried about the situation with our players. We will take our own decision.
"The players we want to keep will stay here next season, we will keep them and the players we want to sell, we will sell if we want.
"But always it's a club decision and we are not worried about the rumours."
Tottenham go into the close season off the back of the club's best performance since the creation of the Premier League in 1992, with the North London side finishing second in the league behind Chelsea.
Pochettino's team ran out easy 4-1 winners over Hong Kong champions Kitchee in a friendly on Friday evening played in front of just over 27,500 fans at Hong Kong Stadium.
Son Heung-min, Vincent Janssen, Harry Kane and Kazaiah Sterling scored for Tottenham, while Brazilian Lucas claimed a consolation for Kitchee.
(Reporting by Michael Church; Editing by Hugh Lawson)
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