Pogba's future at Old Trafford has been called into question after a turbulent 2017-18 season in which he clashed with manager Jose Mourinho, who dropped Pogba from his starting XI multiple times.
The France midfielder, who starred in his country's World Cup triumph this summer, has been linked with a return to former club Juventus, as well as Spanish champions Barcelona.
Pogba added more fuel to the fire after scoring in Manchester United's season-opening win over Leicester on Friday.
"There are things I can say and there are things that I cannot say, otherwise I will get fined," he told reporters when asked if he felt comfortable at United.
Despite the speculation, Braida said his side are unlikely to make a play for the midfielder.
"I don't think we're going to move for Pogba, but he's a great player," he told Radio Sportiva.
Though he has suggested all is not well at United, Pogba insisted that he will continue to give his all for the club.
"I always give my best for the fans, for the team-mates and for the people that trust me," Pogba said following the Leicester match.
"With the players that we have, of course we're Manchester United, we have to look at the top of the league. That's obvious."