Brazil midfielder Bruno joined from Newcastle United this month for a fee put at £75 million by British media. The 28-year-old applied ice to his leg after he came off in Sunday's Community Shield win over Manchester City.
"It's evolving well, but let's see," Arteta told reporters on Thursday about Bruno's fitness problem.
Injuries threatened Arsenal's title charge last term as they missed key players at crucial times, with Kai Havertz, Martin Odegaard, Gabriel Jesus and others absent for long periods.
"The more dominant we are, the bigger the margins, the better... we need to improve the availability of the squad in certain areas in order for those margins to become much bigger," Arteta said.
Arsenal, third on the all-time list with 14 English top-flight titles, have never retained the Premier League trophy, although they won three championships in a row back in the 1930s, but Arteta said this season feels different.
"I feel good. Different. Hopefully better. More excited than ever, hungrier than ever... I have no question that our players have the desire. Now it's something we have to do daily," he said.
'Difficult' transfer decisions to make
Arteta said Arsenal were trying to reinforce their defensive options amid media reports saying they have agreed a £51 million deal with Aston Villa to sign England centre-back Ezri Konsa.
"When we're ready to announce something, we'll let you know," the Spaniard added.
Arteta also put to bed reports linking the versatile Myles Lewis-Skelly with a move away from Arsenal, saying he was "100% sure" that the 19-year-old would remain at the club.
But the manager acknowledged that some players might have to leave, amid speculation that Gabriel Martinelli, Gabriel Jesus and Ethan Nwaneri could depart.
"It's a really, really tough moment... but you have to face it with a real honesty and transparency," he said.
"We all know everything has a start and an end. When it ends, our job and duty is to do it in the best possible way, with respect and admiration for the player and the relationship.
"But at the end, we need to make difficult decisions."