Gremio have reportedly held talks with Real Madrid over the possibility of the club signing Arthur, having grown angry at Barcelona's approach for the midfielder.
According to Marca's Jose Felix Diaz, Los Blancos have scouted the 21-year-old and he has impressed them with his performances, and "they consider his hypothetical addition to be an interesting one."
Gremio were said to have been "infuriated" by the leak of a photo of Arthur donning a Barcelona shirt alongside the club's sporting director Robert Fernandez. Football journalist Paulo Freitas shared the picture on Twitter:
The Brazilian outfit want his €50 million release clause to be met by any interested parties, but Diaz reported they may not get their wish as they're under pressure to sell because of their "delicate financial situation."
Real will play Arthur's Gremio in the FIFA Club World Cup final on Saturday, with the midfielder is missing through injury.
He played a key role in their qualification for the tournament, having helped them win the Copa Libertadores final.
The midfielder was taken off after 52 minutes in the second leg of the final, but as Goal's Dan Edwards and South American football expert Rupert Fryer noted, he certainly left his mark on the match:
OptaJavier provided the stats to back up their assessment:
Arthur excels at dictating the tempo from deep with his impressive reading of the game and metronomic distribution, making him just the kind of player Barcelona have needed since Xavi Hernandez moved on in 2015.
It is also perhaps time Madrid started their search for a long-term replacement for Luka Modric, who has been one of the world's best midfielders in recent years but is now 32.
Arthur looks to be an excellent prospect after a sensational year with Gremio, to the point it appears he could indeed be an asset for a club the size of Madrid or Barca.
What's more, his capture would allow Real the opportunity to scupper the plans of their bitter rivals, so it would be an even better piece of business than simply recruiting a strong player.