The former Gremio midfielder has not featured for Barca since his transfer was announced in June and did not return to training following the conclusion of LaLiga.
Arthur has been left out of the Barcelona squad to face Napoli in the second leg of their Champions League last-16 tie on Saturday and is reported to be hoping to negotiate the termination of his contract.
"It was a surprise to everyone that Arthur did not return," said Busquets, who will be unavailable to face Napoli due to a suspension triggered by a booking in the 1-1 draw in the first leg.
"Arthur's situation has been difficult, but the only ones who know the situation are the player and the club.
"We know some of the news from what comes out, that he left and will now return, but we are on the sidelines and we hope they reach an agreement that will be the best for all.
"We will only focus on the game against Napoli."
Head coach Quique Setien said of Arthur: "I spoke with him before he left, the reality is that from then on I have not spoken to him again, what I have learned has been through the club. I would have liked it to be different, but I can't say anything else."
Barca held a two-point advantage at the top of LaLiga when the season was paused amid the coronavirus pandemic but ended up finishing five adrift of champions Real Madrid.
Captain Lionel Messi made it clear they needed to improve to have a chance of getting past Gennaro Gattuso's Napoli and held talks with Setien to clear the air ahead of the resumption of their European campaign.
Busquets said: "Everything that is discussed in the dressing room to improve is welcome. These weeks have been very good for us to train, to better plan the game tactically.
"We really want to be able to continue in this competition and be in the final eight, but first we have Napoli, who have a great coach and he's not going to make it easy for us."
It remains unclear whether Setien will still be at the helm for the start of the 2020-21 season, but Busquets believes it will be a positive sign for everyone at the club if he is retained.
"It's a decision for the club whether Setien continues or not," he said.
"If Setien continues it will be a good sign for everyone, but that should not worry us now."