According to Mundo Deportivo's Fernando Polo (h/t the Mirror's Liam Prenderville), Raiola recently visited Barca's training ground to discuss his players and some of the club's young talent, and he also took the opportunity to offer them Pogba.
Barca are said to have been interested in him back in 2015, but they failed to prise him from Juventus.
According to Calciomercato,com's Kaustubh Pandey, the Bianconeri are also interested in bringing him back to Turin. But it's also said United manager Jose Mourinho considers him to be "untouchable" and will not sell him "at any price this summer."
The midfielder had an up-and-down season at Old Trafford, struggling to produce his best on a consistent basis—perhaps not helped by Mourinho, who rarely appeared to set up his team with the goal of unleashing Pogba's potential.
He has had a fine FIFA World Cup with France, though, and could lift the trophy on Sunday if they beat Croatia in the final.
Bleacher Report's Sam Tighe praised the 25-year-old during the group stage:
He has been even more impressive in the knockout phase, with strong performances against Argentina, Uruguay and Belgium.
Squawka Football shared the numbers behind his showing in the most recent of those:
Because he can be so effective in the final third, his defensive work rate and contributions sometimes feel underrated, but they have been on show in Russia.
Football writer Liam Canning is hoping Pogba can show more in an attacking sense next season at Old Trafford:
The France international contributed six goals and 12 assists in all competitions last season, but he could reach new heights in the right circumstances.
It's possible Barcelona could provide them, and he has the technical ability to fit in at the Camp Nou.
He also possesses a 6'3" frame and could add more physicality in midfield than the Blaugrana typically deploy, strengthening their spine.
Barcelona still have the money they would have spent on Atletico Madrid star Antoine Griezmann before he opted to stay in the Spanish capital, and a sizeable offer could test Mourinho and United's resolve.
However, the Red Devils have already lost Michael Carrick to retirement this summer, and selling Pogba would require an unplanned dip back into the transfer market for another midfielder.