Pogba – who wore the captain's armband and scored in United's Premier League season-opening 2-1 victory over Leicester City – has endured a strained relationship with manager Jose Mourinho and the Frenchman raised further doubts over his time in Manchester when he claimed he would be fined if he said what he wanted to following Friday's clash.
While the Premier League window closed on August 9, Spanish clubs have until August 31 to complete deals.
Asked about Pogba following Barca's 2-1 win against Sevilla in Sunday's Supercopa de Espana, 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."
Barca have been busy in the transfer market, signing Malcom, Arthur, Clement Lenglet and Arturo Vidal.
The La Liga giants are reportedly still keen to bolster their midfield after club great Andres Iniesta left for Japanese side Vissel Kobe.
Spanish Super Cup champions, first trophy of the season. A title that places Messi as the player with most honours in Barça's history, Congratulations to all Barça fans and to our captain! https://t.co/f16DVY6APN— Josep Maria Bartomeu (@jmbartomeu) August 12, 2018
"We are never going to find another Andres Iniesta, that's impossible because there is only one and he is in Japan," Barca head coach Ernesto 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."