Arthur, 21, has been strongly linked with a move to Catalonia for several months and angered officials at Gremio when he was photographed wearing a Barca jersey in a meeting with its sporting director Robert Fernandez at the start of December.
Barca was quick to offer an apology to the Copa Libertadores champion, reportedly keen to remain on good terms with Gremio in anticipation of negotiations eventually getting started.
While Bolzan confirmed there have been talks, he swiftly highlighted that even if a deal is struck between the two clubs, Arthur – who reportedly has a €50million release clause – will not be leaving before the end of the year.
"At this moment it's [transfer talks] stopped," Bolzan said. "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."