The La Liga champions have been linked with a swoop for the World Cup winner.
And now Barcelona vice president Jordi Mestre has claimed he has read that Pogba is unhappy and refused to rule out moving for the midfielder.
Mestre said: “We do not talk about players that are not at our club.
“What I read is that Pogba is unhappy at Manchester United and his agent, Mino Raiola, has been more vehement in efforts to sell him.
“But I have not read that he says he wants to sign for the club. Yes, he is a player of unquestionable quality in the eyes of all the world.”
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Pogba’s agent Mino Raiola held talks with Nou Camp bosses about a possible deal for the midfielder to leave Old Trafford.
But Manchester United held firm, making it clear Pogba was going nowhere and not for sale at any price.
But it has emerged Pogba has held clear-the-air talks with United boss Jose Mourinho in a bid to repair their damaged relationship.
Pogba had admitted he would be fined if he opened up on his relationship with the United boss after the opening game of the season.
But it is now understood Pogba and Mourinho have made a pact and he will not look for a move in January.
In return, United have agreed not to discuss his immediate future and will address the issue next summer.
But Barca have made no secret of their desire to sign Pogba and not disguised their strong interest in him.
Luis Suarez and Gerard Pique have both gone public on Pogba and talked up Barca’s chances of landing the 25-year-old.
Suarez said: “Pogba’s an elite player who’s won everything.
“He has a lot of quality and he’s one of the references at United.
“I think he would like to be competing for more than he is at the moment. He’s not a player that belongs to Barca, but he would always be welcome.”
And Pique said: “We would be happy to have him (Pogba) here.
“I know little about what he is going through in Manchester and the relationship that exists (between Mourinho and Pogba).
“Pogba is a very good player, but a Manchester United player right now and we’ll see if something happens in the future.”