Juventus have agreed a £72.5m (€80m) fee with Barcelona to sign Arthur - but must still convince the player to join them.
Despite the Brazil midfielder last month telling both clubs he did not want to leave, the Italians are still hoping to persuade him to become part of Maurizio Sarri's team.
Sky Sports News has been told Sarri wants to build his midfield around him in a similar way to that of Jorginho at Napoli and Chelsea.
They have also offered the 23-year-old more wages than his current deal at Barca. According to Sky Italy, that offer is £4.5m (€5m) a year.
Arthur is expected to play for Barca on Tuesday against Athletic Bilbao, and Sky Sports News has been told his preference is still to stay at the Nou Camp and fight for his place.
The two clubs are also said to want to conclude the transfer before June 30 - but Juve sporting director Fabio Paratici has denied this.
He has admitted publicly, however, that the player still needs to be convinced.
Barcelona also want to sign Miralem Pjanic from Juventus and talks are continuing over his valuation.
According to Sky Italy, Juve value the 30-year-old at £63.4m (€70m) but Sky Sports News has been told Barcelona do not feel he is worth just £9m (€10m) less than Arthur.
Barcelona need to sell players to raise funds for new recruits of their own this summer.
A string of their first-team players are on the market including Ousmane Dembele, Philippe Coutinho, Ivan Rakitic, Samuel Umtiti and Nelson Semedo.