The 28-year-old has a year left on his Manchester United contract and is being increasingly linked with a PSG transfer.
If Barca consider themselves serious contenders for Pogba, let's take a look at why a swap deal wouldn't be good news for United.
United's problem positions identified
Who could Barca offer?
Now that Lionel Messi is out of the picture, Griezmann remains the most valuable option.
He is a tireless runner, meaning he can track back and aid with defending if needed. He's versatile and can score some beauties but he's a central attacking midfielder by trade - which is Bruno Fernandes' position.
Unfortunately, Griezmann is not very consistent when he plays on the wings or as a striker. He scored 13 times in La Liga last season but doesn't really address any of our immediate concerns.
His staggering weekly wages around €689,040 mean United should just run as far as they can in the opposite direction.
Once touted as the next big thing in football, Dembele's career has been hampered by a string of injuries. He often injures his hamstring in addition to being plagued by at least five-six other issues. Take a look at his injury record:
The 24-year-old is versatile and can play anywhere in the attack - but again, he wouldn't add much value to our squad.
Having registered just six league goals and three assists last season and those numbers are hardly enough for a Barca player. After signing Jadon Sancho, Dembele is simply not needed at United.
Even if we can forget his past association with Liverpool, Coutinho has been far from consistent at Barcelona.
To be fair, he's been good in flashes - for example, he did decently enough at the beginning of last season. He created chances, tried to score and even made a few goal contributions. But United don't need another player in an already stacked midfield unit.
On second thought, we can't forget he played for Liverpool and then left them to win more trophies with a different side.
Wan-Bissaka leaves a lot to be desired while attacking and Dest would solve that.
The 20-year-old could be sold now that Barca have signed Emerson. Furthermore, Sergi Roberto remains the Catalans' trusted right-back player, leaving the door open for Dest.
However, it's worth noting that the youngster is better at going forward than defending - basically, the opposite of Wan-Bissaka.
Since we are in the market for a new centre-back, Lenglet could've been a back-up option. He can be good on the ball but lacks pace, meaning he's unlikely to make things easier for Maguire.
United are nearing a deal for Raphael Varane and it wouldn't make sense to add Lenglet when we have Bailly, Lindelof and Axel Tuanzebe.
Often dubbed the 'new Pogba', he's a physical midfielder and only 18. Moriba has a long way to go and there are certain areas he needs to improve.
For example, his ball control is very poor and his decision-making could be better too. That comes with age, of course, and United could swap him as he struggles to extend his contract with Barca.
However, would replacing a player like Pogba with a teenager sound logical? Absolutely not.
And none of the players we've mentioned above are worth swapping Pogba for. That doesn't mean the Frenchman won't leave though.
A move to PSG remains on the cards and it will be interesting to see how it plays out.