A £25 million ($31m) release clause in the Belgium international's contract is widely reported to have expired with less than two weeks to go until the end of the transfer window.
The defender insisted his attention is fully focused on Tottenham when asked about his future earlier this week.
Alderweireld was named captain when Spurs beat Juventus 3-2 in the International Champions Cup and the 30-year-old made an appearance from the bench in the 2-1 defeat to Manchester United on Thursday.
Speaking after that loss, Pochettino told reporters when asked about Alderweireld's situation: "Nothing to say about that. I am very focused on working with the players that we have and the club provide us, the coaching staff, and try to help them to improve and work with the players who we are going to have at the end of the transfer market.
"My position from now for the future so you know, otherwise every time... I'm not going to talk about signing players, selling players, extending the contract of the players or not extending the contract of the players. That is going to be all through the club to update you if they want.
"I'm not going to communicate or talk about that, I'm going to talk about managing the squad that we have. To make clear because in the future if you're going to ask me it'll be a little bit weird because I won't answer because I don't have the answer."
Pochettino was forced to apologise to United after his side put in a number of aggressive challenges, including an incident in which Moussa Sissoko appeared to stamp on winger Daniel James.
The Argentine was buoyed this week, though, by chairman Daniel Levy freeing up funds for big investment into the playing squad.
Tottenham had not signed a player since January 2018 prior to the current window, but they have already spent £63m ($78) on Tanguy Ndombele this summer and Paulo Dybala has been heavily reported as the club's next major signing.