Earlier this week the Spanish publication reported that the two clubs reached an agreement for the 21-year-old midfielder to move to the Nou Camp during the January transfer window of 2019.
Barcelona technical secretary Robert Fernandez travelled to Brazil over weekend and Sport said that he and club representative Andre Cury met with Gremio officials on Monday [19 February] night to iron out the terms of a deal which could rise to €40m (£35.4m, $49.3m) with add-ons.
Arthur has a €50m release clause in his contract [Goal.com] but the La Liga giants have managed to lower that fee by allowing Arthur to remain Gremio on loan for the remainder of 2018.
Sport thus say that the transfer will be completed in a deal worth €30m plus €10m extra in variables, with €5m to be paid when Arthur plays a certain amount of games for Barcelona and the remaining €5m if the midfielder signs a contract renewal with the Spanish league leaders in the future.
Now the Catalan publication says that the promising midfielder will complete his medical on Wednesday to take another decisive step towards the deal being completed.
Sport says that the personal terms between Arthur and Barcelona were agreed weeks ago but Fernandez and the promising midfielder are still expected to have a new meeting to reaffirm those terms.
If the reports are correct Arthur will join Barcelona in January 2019 and assist the Catalans in the second half of the season.
Phillipe Coutinho will first need to obtain Portuguese nationality through his wife as, at the moment, Ernesto Valverde already has the maximum three non-EU players in his squad, made up of the former Liverpool star, Brazilian Paulinho and Yerry Mina.
Chelsea, Manchester United [Daily Mail] and even Real Madrid [Marca] have also been linked with Arthur in recent months with the midfielder tipped to be the as one of the next big thing to emerge from the prolific Brazilian academy.
However, Barcelona have been leading the race since December when the player was photographed in a Blaugrana shirt alongside Fernandez after the technical secretary travelled to South America to watch him in action during the two-legged Copa Libertadores final between his side and Lanus.