Barca were said to be nearing a £26m deal to bring the 21-year-old to Camp Nou in time for next season, having supposedly seen off competition from a number of other European suitors.
Gremio president Romildo Bolzan Jr has confirmed that the two sides have previously been in discussions, but a transfer will not go through for Arthur - yet to be capped at senior level by Brazil - until the Campeonato Brasileiro Serie A season concludes.
"At this moment [transfer talks] have stopped," Bolzan told UOL Esporte. "But I can tell you that all the ideas are Arthur will stay with us until December.
"All parties agree that it is more or less agreed that Arthur will stay until the end of 2018 if the negotiations are completed. I repeat, if they are completed."
Barcelona issued an apology last year after Arthur was spotted wearing a club jersey during talks with sporting director Robert Fernandez.