The 20-year-old defender has been the subject of interest from Brighton but the Blues have rejected each of their advances, and insist he is not for sale.
Chelsea have also seen transfer bids up to £70million rejected by Brighton for midfielder Moises Caicedo, with the Seagulls insisting he is worth around £100m.
Pochettino said: “With Levi, we were also talking. It was a nice talk.
“Of course, it was private like with other players but it is important that they need to know us, know what we think, to see that the competition will be tough but to challenge for that and know they can be in the starting XI. Because football is about competing.
“They understood and we understood what they wanted to translate to us. All is clear and we are happy with all the players we have in the USA.”
Romelu Lukaku, Hakim Ziyech and Pierre-Emerick Aubameyang all trained at Cobham on Tuesday as 29 of their teammates worked out in front of a crowd in Chapel Hill, North Carolina ahead of the pre-season match against Wrexham.
Chelsea saw Inter Milan’s approach for Lukaku collapse over the weekend but Pochettino is comfortable with the situation that has led to three senior stars training away from the group.
“This situation is [like this] because everyone agrees,” he added. “The club will find the best solution for everyone. The decision that we made was also decided by the players. I think both the club and player are in a position that they wanted.”
The average age of Chelsea’s current squad is just 21 but they are working to sign a host of reinforcements.
Pochettino refused to speak specifically about Caicedo but has admitted he is open to signing a defender after Wesley Fofana underwent surgery on a major knee injury. He said: “It is obvious that we feel sad for him first but then because he is an important player for the squad.
“We have to think and see if we stay how we are or whether we need to work to add a player but it is not sure.”
Chelsea have signed Christopher Nkunku, Nicolas Jackson and a host of younger players but need more after successfully selling 12 major first-team stars this summer.
Pochettino hopes business can be done quickly but prefers the right targets arrive at a slower pace, adding: “I want the right profiles to arrive to improve the squad.
“Of course as soon as possible is better than later but we want the targets we want to have. Today is better than tomorrow but we know it is difficult.”
