The Blues have high hopes for the young center half, who has been praised by the likes of John Terry recently.
Asked about Gilchrist, Pochettino told reporters: "Look, I think it's good for a player who came through the academy. You can see how he feels the shirt and the badge, Alfie, and congratulate him for getting a new contract.
"And for the second part of your question, I think it is a player who arrived now and is of course doing well. But I don't know, he is like five, six or seven years on his contract. I don't know. But no worries that the club believe they need to compensate or reward players, I'm sure the club is going to do.
"He is playing football. That is why we bring him (here) to play football. He is an offensive player who is doing well. This is always the idea when we sign players, to perform in the way that he has performed."