Sky Sports in Italy are reporting that United have been offered £45m and the Barcelona duo of defender Yerry Mina and midfielder Andre Gomes in exchange for Pogba.
Pogba shone for France in the World Cup as the 25-year-old re-established himself as one of the world's best midfielders after a frustrating season for United.
Reports have emerged in recent days that super-agent Mino Raiola has been touting his client around.
Paul Pogba's relationship with José Mourinho is under strain again.
United are aware that it could be a ploy by Pogba's representative to secure him a new contract on the same terms as £500,000-a-week top earner Alexis Sanchez.
Paul Pogba has been linked with a move to Barcelona - but who could replace him at Man Utd?
"I think the World Cup is the ideal habitat for a player like him to give [their] best", Mourinho said. Mourinho appeared to question Pogba's effort and heart while playing for his club, saying, "I don't think it's about us getting the best out of him [at Manchester United], it's about him giving the best he has to give".
'The players are in a closed camp, isolated from the external world, from commercial compromises, and every possible influence'.
But, Gianluca Di Marzio.com claim Barcelona have made the first move to sign Pogba by offering a player the club knows United would like.
Pogba moved to Manchester United in the summer of 2016 for a then-record $121 million, and has been stuck with massive expectations ever since.
FC Barcelona could feasibly complete a deal to sign Pogba any time between now and the end of August, when the European transfer window closes.