The Brazilian publication says that all parties are "optimistic" over reaching a deal with the La Liga giants having already agreed personal terms with the 21-year-old midfielder.
Chelsea and Manchester United [Daily Mail] have both been linked with Arthur in recent months but Barcelona have been the front runners in the race since early December when the player was photographed with a Blaugrana shirt alongside club technical secretary Robert Fernandez.
Last month, Mundo Deportivo reported that the Catalans had sent representative Andre Cury to Brazil to step up negotiations with Ernesto Valverde's side having identified Arthur as priority target for the future of the club.
Earlier this week, the Spanish publication provided a major update after claiming that Barcelona have already an agreement in place with Arthur for the Gremio starlet to move to the Nou Camp during the January transfer window of 2019.
The Catalans already have the maximum of three non-EU player in the squad in Philippe Coutinho, Paulinho and Yerry Mina and plan to wait for the former Liverpool star to be awarded Portuguese nationality to make space for Arthur.
UOL Esporte is now supporting the information from Mundo Deportivo, confirming that Arthur has already agreed the personal terms over a five-year deal to move to the Nou Camp ahead of the second half of next season.
And the Brazilian publication says that Barcelona officials are expected to travel to Porto Alegre next week in the hope of reaching an agreement with Gremio over the transfer.
UOL Esporte says that the Brazilian outfit are demanding around €30m (£26.6m, $37.4m) plus add-ons for 60% of his rights with the remaining 40% belonging to third parties.
Gremio president Romildo Bolzan Júnior has claimed that he is unaware whether Arthur has already reached an agreement with Barcelona but the chief made it clear that the deal between the clubs is yet to be agreed.
"We were not told Arthur was sold. I will take into account that it is a journalistic matter that may have come from internal sources. But there are negotiations and there are advances in some parts of the negotiation," Bolzan said as quoted by Globo Esporte.
"One of them is that Arthur will stay with us for a while but Gremio have not finalised and does not have a definite proposal. I will leave [this] as press speculation, not a business situation. Grêmio have not completed deal with Barcelona."