However, the Spanish champions may return with a "vastly improved" offer for Pogba either in January or next summer, according to Jason Burt at the Telegraph.
Barcelona can afford to make a big-money move for Pogba. They have funds available after missing out on Antoine Griezmann earlier this summer, according to the report.
Manchester United have already rejected a bid from Barcelona of €50 million (£44.7 million) plus Yerry Mina and Andres Gomes for Pogba, per Burt.
Football writer Jordan Clarke offered his view on the offer:
Pogba cost Manchester United £89 million when he re-joined the club from Juventus in 2016. He won the 2018 FIFA World Cup with France in the summer, scoring in the final, meaning his stock is currently high.
However, there is a suggestion all is not well at Manchester United under manager Jose Mourinho. The Portuguese dropped the midfielder on occasion last season and hasn't been able to consistently get the best out of him.
Pogba was asked if he is "happy and comfortable" at Old Trafford, per Rob Dawson at ESPN FC. He said: "There are things, and there are things that I cannot say, otherwise I will get fined."
He also posted a cryptic message on Twitter:
Mourinho made Pogba captain for Manchester United's first Premier League game of the season against Leicester City on Friday. The midfielder scored the opening goal from the penalty spot in a 2-1 win.
The Red Devils boss described him as a "monster" after the match, per Jack Wilkinson at Sky Sports.
Mourinho is said to be unhappy with Pogba's agent, Mino Raiola, who he believes has been "hawking" the midfielder around Europe, according to Paul Hirst at The Times.
Barcelona have invested heavily this summer by bringing in Arturo Vidal, Arthur, Clement Lenglet and Malcom. The club are interested in Pogba but "are not willing to break the bank" for the 25-year-old, according to Ben Hayward at the Evening Standard.
There does appear to be tension between Pogba and Mourinho, and his future may depend on what happens on the pitch this season. If the situation continues, Manchester United may face a real challenge keeping hold of their World Cup winner.