As reported by Gianluca Di Marzio, Barca have offered €50 million for the Frenchman, plus centreback Yerry Mina and midfielder Andre Gomes.
Pogba came through the youth system at United before leaving for Juventus on a free transfer.
Back in 2016, the 25-year-old completed his move back to Old Trafford for a-then world record fee, but things could have been very different according to one of Barcelona's directors.
It has been claimed that Pogba's agent Mino Raiola has already agreed the outline of personal terms on a contract with Barcelona and a €110m deal could be done.
United can still receive offers for players after Thursday, but will not be able to pursue targets to replace Pogba.
Paul Pogba's relationship with José Mourinho is under strain again.
Thoughts on Barcelona's cash plus players offer for Paul Pogba? With that out of the way he's coming good though we all know he can do even better.
"Why? Because it's closed for a month, where he can only think about football".
With Mourinho known for not staying at a club for longer than three seasons, fans seem to be wary ahead of his third campaign at United. Where he's with his team on the training camp, completely isolated from the external world, where they focus just on football, where the dimensions of the game can only motivate.
He goes on to report that United do not want to sell the "important" player as they see him as the franchise of the club.
The deal could hinge on Marcos Rojo leaving United and he has yet to be convinced that a move to Everton is the best option for him.