Tottenham are the only Premier League club not to have made a signing ahead of Thursday's deadline but there were reports on Tuesday evening they had made a £25million move for Aston Villa's Jack Grealish.
In an attempt to lure the midfielder to Camp Nou before the close of transfer window, the Catalan giants have also tasked Pogba's agent Mino Raiola to facilitate the deal as fast as possible.
Manager Jose Mourinho has already predicted a "difficult season" if United do not do more business, so losing a World Cup-winning midfielder would only add to that.
The Sun claims he has told United he wants a £200k-a-week pay rise if he has to stay. The 31-year-old won two titles at the Etihad Stadium but fell out of favour after the arrival of Pep Guardiola as manager in 2016.
Essentially, though, Pogba's unhappiness stems from the deterioration in his relationship with Mourinho, who not only does he blame for his muted performances for United since his move but also for his qualified praise of his performances for France at the World Cup.
But the story does go on to claim that through Raiola the Frenchman has agreed a bumper deal worth £89.5m over five years with Barcelona and "has his heart set" on joining the club. The Belgian had been due to return on Monday after a delayed summer holiday following the World Cup.More news: Republicans Spent Big to Win a Special Election. Now They're anxious
Pogba, who did not accompany United on the US tour, will meet Mourinho this week after returning to United's Carrington training centre Monday after a three-week break following France's World Cup triumph.
The 29-year-old defender is believed to have contacted Mourinho personally to explain his disinterest in making the move - increasing speculation that Boateng is holding out for a switch to Ligue 1 moneybags Paris Saint-Germain instead.
A number of United's under-23 squad could make temporary exits, with European leagues remaining open for business and English Football League clubs allowed to make loan signings until the end of the month.
Have Manchester United been given fresh hope in their bid to sign Leicester City defender Harry Maguire?
The Chilean scored just three times in 18 games as United ended the season without a trophy. On Sunday, some British media, such as the BBC and the Daily Star, say the deal could happen next week.