The Spanish publication claims in its Wednesday's front cover (14 February) that the La Liga giants will now try to convince Gremio complete the deal but they add that the negotiations between the clubs are on track.
Arthur has been tipped to join Barcelona since early in December he was photographed with a Blaugrana shirt alongside club technical secretary Fernandez after the Catalans' chief travelled to South America to watch him in action during the two-legged Copa Libertadores final between his side and Lanus.
The La Liga giants were then even forced to issue an apology and speculation subsequently cooled.
In January Barcelona focused their attention on the signings of Philippe Coutinho and Yerry Mina with Arthur seemingly a target for the future.
But those talks talks have resurfaced in recent days since on 26 January Mundo Deportivo themselves broke that Barcelona had sent representative Andre Cury to Brazil to step up negotiations with Gremio.
Days later Gremio executive football director André Zanotta confirmed negotiations had begun with the club but earlier this month club president Romildo Bolzan gave a contradictory update on the saga.
Bolzan said that talks between the clubs were stalled but at the same time admitted that all the parties had agreed that even if they finally reach an agreement Arthur will continue at Gremio for the remaining of the year.
"At this moment the [transfer talks] have stopped," Bolzan told UOL Esporte. "But I can tell you that Arthur will stay with us for another year [until December]. All parties agree on that. It's more or less agreed that Arthur will stay until the end of the year  if the deal is completed. I repeat, if it is completed."
Mundo Deportivo are now supporting Bolzan's comments claiming that Barcelona have reached an agreement with Arthur for the player to join them in January 2019.
The Spanish publication claims that Barcelona ironed everything with Arthur's agent Jorge Machado and his family during the trips made by both representative Cury and club technical secretary Fernandez to Brazil.
The report adds that negotiations between the clubs are also on track but will be more complex with Arthur's rights being shared between Gremio (60%), a investor called Celso Rigo (20%) and his family (20%).
Mundo Deportivo says that Gremio are demanding at least of €30m (£26.7m, $37m) for the 60% of his rights with the player having a €50m release clause in his contract.
Barcelona would also need to pay a part to Rigo while the Spanish publication understand that the remaining 20% which belongs to his family won't be an issue to complete the deal.
It appears Barcelona will have to pay in excess of €30m to complete his signing despite originally intending to sign him for around €25m.
Meanwhile, earlier this week Coutinho told Mundo Deportivo that is set to apply for the Portuguese nationality in order make a space for another non-EU player in Ernesto Valverde's squad.
The Catalans have already reached the three-player limit after signing the Liverpool star, Brazilian Paulinho and Yerry Mina.
Mundo Deportivo says that if Coutinho doesn't get the Portuguese nationality before January 2019 Barcelona would need to decide whether to allow Arthur to stay at Gremio or loan him out to another European club.