The playmaker was pictured in a Barca shirt earlier this week as reports claimed that a move to the Camp Nou was as good as done, however, Gremio have denied those claims and sent a message of defiance to the Catalan side.
"If Barcelona want to sign Arthur, there is a release clause in his contract. If they pay it, he's theirs," the club's vice president Romildo Bolzan told 'RAC1'.
"Arthur has a contract with Gremio and a release clause of €50 million. If they (Barcelona) pay that we can't do anything but there is no conversation or negotiations open," he added.
The 21-year-old midfielder met with Robert Fernandez and Andre Cury this week and Bolzan admitted that Gremio had authorised the meeting.
"They told us that Arthur was going to eat with some representatives from Barcelona and we authorised the encounter because it was just to meet the family, nothing more," he explained, before adding: "Gremio are not comfortable with this situation."
Arthur's style of play has been compared to Barca legend Andres Iniesta, but will the La Liga leaders stump up the money to secure a deal?