Pogba has been linked with a move away from Manchester United in the summer, with Barcelona one of the clubs reportedly circling.
The World Cup winner has registered his best season to date in England, scoring 13 and assisting nine in the league, which earned him a spot in the PFA Team of the Year.
Pogba himself has flirted with the idea of joining Real Madrid but Los Blancos’ rivals are still seeking a remedy for their post-Andreas Iniesta midfield troubles.
Speaking to Sky, Mestre said: “Everyone likes Pogba.
“But not every player that we like comes to Barcelona.
“I like him a lot, you can’t question the quality that Pogba has.
“But you could say the same about [Mohamed] Salah or [Eden] Hazard – they’re world class.
“But not all world class players, and those that I like, come to Barcelona.
“What we need to do is make sure those that are with us at the moment are very happy.”
There have been suggestions Ivan Rakitic could depart in the coming months in order to free up a midfield spot and somewhat subsidise a transfer fee for a marquee signing.
Mestre tried to diffuse those rumours, though.
“Rakitic has a contract, we renewed it last year,” the Nou Camp white-collar said of the Croatian, whose deal expires in June 2021.
“He’s a great player, a very important one in the squad and he’s a sensational person. We’re in love with Rakitic.”
Mestre also denied that Ajax starlet Matthijs de Ligt has already signed for the Catalans amid strong interest from the club.
“I don’t know why they’re saying this because [De Ligt] hasn’t signed,” Mestre said.
“[Gerard] Pique is evidently one of the best central defenders in the world, if not the best.
“After him, we have players like [Clement] Lenglet, [Samuel] Umtiti and we’ve signed a very young player in [Jean-Clair] Todibo. The defenders we already have are of the highest level.”