Officials from the Catalan club travelled to Milan on Wednesday 1 July to meet with their Juventus counterparts to iron out a deal for the France international.
The Champions League winners are unable to make any additions during the current summer transfer window due to a Fifa ban so, according to the Spanish publication, the agreement will see Pogba joining them next summer.
The Catalans had indeed previously signed Aleix Vidal from Sevilla despite him not being able to play until January and had earmarked the signing of Pogba as their next top priority.
The club will hold elections to choose a new president on 18 July and all the candidates have admitted the signing of Pogba is a priority for manager Luis Enrique.
Even though it is still uncertain who will take charge of the team next month the current staff have been working to fulfil Enrique's demands and outbid the Premier League giants for Pogba.
Several Spanish newspapers, including Sport, reported earlier on Wednesday that club director of sporting institutional relations, Albert Soler, and Sporting director, Ariedo Braida, have made a decisive trip to Milan on Wednesday 1 June to meet with Juventus managing director, Guiseppe Marotta, to iron the conditions of the deal.
And later Sport announced the clubs have reached an agreement with Juventus to seal the deal next summer even though Chelsea and Manchester City were also interested in securing his services.
Earlier this week Sport revealed Barcelona will offer Juventus €90m (£63m, $100m) to seal the deal with €80m plus further €10m on add-ons.
The Catalan publication then added that Chelsea bid would include Juventus target Oscar plus €50m and that while City are ready to pay €100m to secure his services Barcelona are the favourites because they offer Juventus the chance to keep Pogba one more season.
Sport points out that the deal will not be completely close until the election of the new president while the club also need to reach personal terms with Pogba.
The Spanish publications say that Pogba is ready to wait until next summer to make the move but is demanding a salary of €12m per season to complete the deal.
Joan Laporta, former club president and one of the favourites to win the coming elections, recently asserted the player wants to play at Barcelona.
"Pogba is very excited to come to Barcelona. I have a very good relationship with [agent] Mino Raiola. It would be one of the best signings. Everyone believes that he would fit into this team," Laporta said during an interview with Catalunya Radio.