The Red Devils are said to have been offered £45m upfront, as well as central-defensive target Yerry Mina and midfielder Andre Gomes.
It is believed Barcelona is working together with Pogba's agent Mino Raiola to secure a deal for the Manchester United midfielder.
The report suggests that the World Cup victor had contacted Manchester United supremo Ed Woodward to tell him that he'd like to leave Old Trafford this summer.
Jose Mourinho wants Pogba back at Old Trafford and is hopeful he can replicate his form on the worldwide stage for United.
The close of the transfer window is just days away and Manchester United still have business to do.
Mourinho has taken plenty of heat for not putting Pogba in a position to succeed at Manchester United, and some have even theorized that if things don't change, Woodward will be tasked with picking one or the other.
Should United eventually accept an offer, Pogba would earn €100m (£100m) over five years at the Nou Camp.
Paper Round's view: United presumably don't want to sell Pogba for a few reasons.
According to Bild, the Germany worldwide is said to have called Mourinho to inform him of his decision after Niko Kovac's plea for the centre-back to remain with the German champions.