Chelsea beat Brighton 4-3 in their second game of pre-season in the United States, with the south coast club making a club-record offer to sign the England Under-21 defender earlier this summer.
Brighton boss Roberto De Zerbi has even claimed Chelsea should release Colwill if they want to sign Seagulls midfielder Moises Caicedo after a number of failed offers from Stamford Bridge.
However, Pochettino insisted he would not accept the idea of selling his 20-year-old defender, claiming: “He will continue with us.
“I am pleased with him, his performance today was very good, better than I expected because it is only our first game after the season against Brighton. I’m very happy, he can become one of England’s greatest centre-backs.”
The Blues won on Saturday night thanks to goals from Christopher Nkunku, Mykhailo Mudryk, Conor Gallagher and Nicolas Jackson.
Pochettino is happy with his pre-season going on with games against Fulham, Newcastle and Dortmund coming up, adding: “It’s about the project, it’s about building a squad capable of creating the space they deserve or the space we believe they deserve.
“Then it’s about quantity, if you have a big squad with 30 skilled players, it’s very difficult for young players to get a place. The important thing is that if we find out that they can use the space we want to create for them, we will of course give them an equal footing.
“We also need to understand that we are at Chelsea. Chelsea is for winning, not for developing players. Of course, we will have some slots available to them with the ability and potential to become a senior player in this football club.
“We need to be careful because everyone expects to win, when you play for Chelsea it’s about winning, not just playing beautiful football.
“Yes, we have a lot of young players but we also need some experienced players. We are working very hard to add some players who can help this year but please help today and try to get what we want. On my side, and on my side, I think I’d love to have these places where they can help them, if we see the potential coming as a senior player for Chelsea.”