The Belgium international moved to North London from Atletico Madrid in 2015 after impressing during a loan spell with Southampton during the 2014-15 campaign.
Pochettino told reporters on Thursday: "He was talking with me in my office this morning. He is happy, he wants to make fully clear his position that he is fully committed to the club.
"He is happy with his contract – two years plus one – but it is not easy.
"I recognise that in the last few days there have been some rumours but he is so happy and so calm. His idea is to try and play here and he has no reason to move."
Manchester City and Chelsea are reportedly monitoring developments surrounding Alderweireld, and both clubs are considering launching offers in the January transfer window.