Barca reached an agreement with the Campeonato Brasileiro Serie A side earlier this year over a price for Arthur, which could rise to around £35m.
Bolzan insists that Arthur is staying put until the end of the Brazilian football season, though, unless his contract is bought out in full.
"There's no chance that Arthur leaves the club in the coming months because it's already written down," he told Sport.
"There's a contract signed and that is not a possibility. Barcelona have never brought to the table any interest in signing Arthur halfway through the [Brazilian] season.
"The only right that Barca have is an option to buy him, in which case they must do the transaction before July 15."