Last week, the Spanish publication reported that the La Liga giants had reached an agreement in place with Arthur for 21-year-old midfielder starlet to move to the Nou Camp during the 2019 January transfer window.
Mundo Deportivo added that negotiations between the clubs were going to be more complex with Gremio demanding around €30m (£26.6m, $37.2m) for 60% of his image rights, with the remaining 40% being shared between investor Celso Rigo and Arthur's family.
Gremio president Romildo Bolzan Junior later claimed that he was unaware whether Arthur had already agreed personal terms with Barcelona but admitted that the clubs had made some progress with regards to certain parts of a potential deal which could see the player move to the Nou Camp next year.
"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."
Mundo Deportivo insist that the clubs are yet to reach an agreement but understand that Fernandez arrived in Porto Alegre on Saturday [18 February] to step up those negotiations.
The Spanish publication adds that Barcelona's idea is to use a similar formula to the one which helped them to secure the services of Yerry Mina from Palmeiras during the recent January transfer window.
Ernesto Valverde's side had first refusal to sign the Colombian international for €9m next summer but they agreed to pay a €2.8m compensation fee to bring the deal forward to fill the gap left by the departure of Javier Mascherano to Hebei China Fortune.
Mundo Deportivo claims that Barcelona will try to earn first refusal to sign Arthur for a set price in the next January window and retain the option to pay an additional fee to bring the deal forward to the summer if Valverde considers it necessary.
The report says the La Liga giants want to strike a deal as soon as possible in order to beat off competition from other clubs and also avoid his price rising in the summer if he plays in the World Cup with Brazil.
Mundo Deportivo says that Arthur also has offers from the Premier League but the player has set his sights on a move to Barcelona.
Indeed, in December the Brazil starlet was photographed with 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.