The France international signed a new five-year contract last July but his stellar performances for Spurs this season have increased suggestions that he will leave White Hart Lane this summer.
But Pochettino believes the 28-year-old goalkeeper wants to stay and that a move away would not be easy.
“Hugo is happy here with us, he’s very happy,” said the Spurs boss.
"It’s difficult for these types of club to get him.
“Hugo is one of the best goalkeepers in the world, and I have recognised that in different press conferences in the past. His contribution is magnificent.”
Pochettino also insists he is happy to keep Emmanuel Adebayor at the club after Spurs chairman Daniel Levy blocked the striker’s proposed loan move to West Ham on deadline day.
“We’re happy too that he stays here because I think he’s a very important player,” Pochettino said.
“We just need to provide him with the tools to improve his game and try to help the team to get their objectives.
“Like all players, [we need] to try to push them, to train them in a good way and then give them the opportunity to play so they can give their best.
“I have confidence in him, like in other players, and then he needs to try to show that on the pitch.”