Barca had been pushing to sign Arthur during the January market, though were happy to continue negotiations into this month.
But Bolzan has now declared talks have been broken off.
"Currently, the case is stopped. I can tell you that Arthur will stay with us for another year," the president stated.
Along with Barca, Gremio officials have warned there are other European clubs interested in Arthur. Barca had pushed to sign the midfielder before the World Cup so to avoid his price skyrocketing should he shine in Russia.