Gremio executive football director André Zanotta says that talks will continue in the coming days but the club chief adds that any potential deal won't be completed until after the current January transfer window ends on Wednesday [31 January].
The 21-year-old midfielder has been heavily linked with a move to the Nou Camp since it emerged that Barcelona technical secretary Robert Fernandez travelled to South America to watch him in action during the two-legged Copa Libertadores final between Gremio and Lanus.
The La Liga giants were then forced to issue an apology to Gremio after a picture of Arthur wearing the Blaugrana shirt alongside Fernandez was leaked though social media.
Last week, Mundo Deportivo reported that Barcelona sent representative Andre Cury to Brazil to step up negotiations.
The Spanish publication claimed that Arthur had an agreement in place to join Barcelona with the club now trying to agree a deal with Gremio to complete the transfer.
Now Gremio chief Zanotta has confirmed that they had a meeting with the Barcelona representatives over the weekend but suggests negotiations will take a while.
"There have been a formal contact and we're going to continue the conversations" Zanotta said as quoted by UOL Esporte.
"We have our conditions. I do not want to give more details, it's a conversation that has just started and it's still going to drag on. Arthur's transfer will not take place before January 31. If the negotiations advance it will not be in the next few days, it will drag on for a few more weeks."
Barcelona can not sign Arthur this month as Ernesto Valverde already has the maximum number of non-EU players in his squad in the form of Philippe Coutinho, Yerry Mina and Paulinho.
But UOL Esporte says that the La Liga giants still want to complete the move as soon as possible in order to avoid a battle in the summer for his services.
UOL Esporte says that the Catalans are set to have a new meeting with Gremio on Monday [29 January] to step up the race for his services.
The Brazilian publication says that Gremio own 60% of Arthur's rights and are demanding around €30m (£26.4m, $37.2m) for them.
However, the Catalans would instead like to pay that fee for 100% ownership meaning negotiations are not expected to be completed before the transfer window slams shut.