Mundo Deportivo claims that the La Liga giants "already have an agreement" in place with the coveted midfielder and will now try to reach a deal with Gremio to complete the transfer.
The Spanish publication says that on Thursday [25 January] Andre Cury took a flight from Barcelona to Porto Alegre to give a final push to the negotiations.
Cury has been working as Barcelona's representative in South America since 2012 and played a crucial role - alongside new Arsenal head of football relations Raul Sanllehi - in the deal that saw Neymar move from Santos to the Nou Camp a year later.
His trip to Brazil comes only days later Mundo Deportivo reported that Barcelona had earmarked the signings of Arthur and Antoine Griezmann as the two priorities for the upcoming summer transfer window.
United, Chelsea and Real Madrid have also been linked with the 21-year-old midfielder in recent times but the Spanish publication said on Wednesday [24 January] that Arthur had already given the green light to make the move to the Nou Camp.
Now Mundo Deportivo insist that the agreement with Arthur is already in place and Cury will try to convince Gremio to cash in on with the player during his stay in Brazil.
Arthur has a €50m (£43.7m, $62.3m) release clause and Gremio officials have publicly stated that any suitors would need to match it to lure him away from his homeland.
The Daily Mail recently claimed that United and Chelsea are also monitoring the situation and it looks like his side will try to use the interest of all those European giants to try to make the most of his sale.
Yet, earlier this week Mundo Deportivo said that Barcelona hoped to sign him for only €25m by offering Gremio the possibility of keeping Arthur on loan one more season.
Arthur is still 21 years old and the Spanish publication said then that he would be ready to wait one more year to complete his desired move to the Nou Camp.
Yet, last month the Brazilian was photographed with a Barcelona 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 Gremio and Lanus.