Pogba threw his United future into doubt on Friday after captaining the side to a 2-1 victory over Leicester City.
Having enjoyed a fractious relationship with manager Jose Mourinho over the past two seasons reports in Spain have claimed the Blaugrana are exploring the possibility of the 2018 World Cup winner arriving at the Camp Nou.
With club icon Andres Iniesta having departed the club, the LaLiga champions are seeking a major investment to fill the boots of the La Roja legend.
Asked about Pogba after Barcelona's 2-1 Super Cup win against Sevilla, President Josep Maria Bartomeu said: "I won't speak of any names, we have respect for all clubs and there are 20 days left.
"We'll see which players come out. We're focused on the league, so it's best to ask [Eric] Abidal, [Ramon] Planes or Pep Segura about players. There's still time to do business."
Barcelona manager Ernesto Valverde did, however, refute the claims that Pogba has been shortlisted as the 'Iniesta replacement'.
"We are never going to find another Andres Iniesta, that's impossible because there is only one and he is in Japan," Valverde said. "I don't think about signings. I think about my team and preparing for the next match.
"That's my plan, although everything is up in the air until the window closes."