The Catalan club have been keen to bring in the 21-year-old for the past six months, ever since he caught the eye in his side's Copa Libertadores triumph.
Barca had initially been warned that they would have to wait until the end of the year before landing the uncapped Brazilian, but it appears as though a transfer could go through before then.
Speaking to reporters on Wednesday night, Bolzan said: "The topic is on its way to being finished. The documents are not signed yet, but the transfer is reaching the final phase.
"I think it will be over by tomorrow or the day after tomorrow. Some things still depend on legal issues. It still requires some care. It is heading towards a final situation tomorrow, I believe."
Arthur, who was also wanted by a string of other European clubs, is understood to be valued at around £35m.