Pogba has scored penalties in both of United's Premier League games this season, wearing the captain's armband in Antonio Valencia's absence.
But reports linking Pogba with a move away from Old Trafford have been unrelenting in the 2018-19 campaign.
Jose Mourinho denied a rift with Pogba after the France international suggested he could not give his honest opinion on club matters without being fined.
And although Barca's head coach Ernesto Valverde has refused to discuss the prospect of signing the 25-year-old, former United defender Pique has opened the door.
"I know very little of what is happening in Manchester, the relationship that exists [between Pogba and Mourinho]," said Pique.
"Pogba is a very good player, but a Manchester United player right now, and we will see in the future if anything happens.
"We would be happy to have him here, but Manchester United is his club and, if someone has to say something, it must be them."
Barcelona are running out of time to complete a shock deal for Pogba as La Liga's transfer window closes on Friday.