Odegaard has been out of action since sustaining an ankle ligament injury while on international duty with Norway in September.
Norway boss Stale Solbakken recently claimed Odegaard was making progress in his bid to recover in time for the next international window in Norway.
Speaking to the media on Tuesday, Arteta gave an update on how Odegaard is faring in his recovery process from an ankle injury.
Arteta provides positive Odegaard update
Odegaard will now be ready for Wednesday's EFL Cup meeting with Preston North End, but Arteta is hopeful that he could return to action before the next international break.
"He's been on the grass for a few weeks, but there is still a few boxes to tick," Arteta told reporters in the pre-match press conference.
"How fast we can do that last stage of the rehab is a question we'll have to answer once we have players around him and he starts competing with the team.
"He hasn't done that yet. Will he be back before the international break? Hopefully yes but we'll have to see how that stage goes."
Arteta not concerned by Gabriel, Timber injuries
Arteta also provided a positive update on Gabriel Magalhaes and Jurrien Timber after the pair were forced off in Sunday's 2-2 draw with Liverpool.
The Arsenal boss seems confident that the defensive duo will be fit to feature in Wednesday's matchday squad at Deepdale.
"We are still assessing Gabriel but it doesn't look bad at all," Arteta said. "He was much better the next day so hopefully he will be fine. He has had some tests.
"Jurrien is fine. He was very tired, he had been out for a while and could not continue the game but there is no new injury there at all. He could not continue so we decided to make a very safe call. But he was fine."
Arteta also revealed that he is handing a debut to young goalkeeper Tommy Setford, who has recovered from a hip injury which has kept him sidelined for most of the season.