The Norway midfielder has been sidelined with an ankle problem suffered on international duty early last month.
Although Odegaard has not played for the Gunners since August 31, Arteta’s side remain unbeaten in the Premier League and are just one point behind leaders Liverpool ahead of Saturday’s game at Bournemouth.
The Spaniard said Odegaard would not be ready for this weekend but the situation will be reassessed ahead of next week’s games against Shakhtar Donetsk, in the Champions League, and Liverpool.
“I think he’s not going to be fit for this game,” Arteta told reporters on Friday.
“Next week will be a different story, but again, in that later stage of rehab where he is at the moment, because he’s doing already a lot of the stuff, he needs to clear some markers, he needs to clear certain things, he needs to be comfortable doing things, especially with the ball.
“I think next week will be crucial to understand how close he is.”
Arteta also allayed fears over the fitness of Bukayo Saka, who was injured during England’s 2-1 defeat at home to Greece last week and missed the 3-1 win in Finland.
The Arsenal boss said a late call would be made over the fitness of the winger.
“It’s not a serious injury,” he said. “He’s evolving really well. He’s done a few things in the last two days.
“He wasn’t fit enough to play with the national team the second game but we are hopeful. We have a training session this afternoon, he did some bits yesterday, so let’s see if he can make it on time.”
Arteta also had positive news on forward Kai Havertz, who was withdrawn from the Germany squad for their games against Bosnia and Herzegovina and the Netherlands over a knee problem.
“He had a few issues and we’ve been dealing with that,” he said. “He’s been absolutely brilliant, he has very good communication with the national team, with the manager.
“They understood the situation, we modified everything that we could do here and again if he trains well today he’s got a good chance to be fit and available.”
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