The former Real Madrid wonderkid has missed the Gunners' last two Premier League fixtures against Tottenham Hotspur and Manchester City after suffering a nasty twist while representing Norway in the UEFA Nations League.
Odegaard was captaining his country against Austria when his ankle buckled during a duel with Christoph Baumgartner, who subsequently apologised for his role in the incident on social media.
Mikel Arteta was initially tight-lipped on how severe Odegaard's problem was, but the consensus was that his issue was a serious one, and the Gunners boss finally confirmed earlier this month that he would be out for "a while".
The club have still not put a timeframe on Odegaard's recovery, although Arteta conceded in Tuesday's pre-game press conference that he does not expect to have the midfielder back in action before the international break in October.
Odegaard: 'Tricky to say when I can play for Arsenal again'
Odegaard will watch on from the sidelines when Arsenal host League One outfit Bolton in Wednesday's EFL Cup third-round contest, and ahead of the visit of the Trotters, the 25-year-old provided a detailed update on the incident and his ongoing recovery.
"It was a bad twist to my ankle, and I damaged some ligaments there, but it's part of football and now I'm just trying to recover as quickly as I can. I'm moving forward, making progress and I'm feeling more positive every day. I'm working hard and my only thought is to get back as soon as possible," Odegaard told arsenal.com.
"I'm at the Sobha Realty Training Centre basically every day now, working hard and doing everything I can do to get better. I have to be careful not to push it too much, but at the same time do what I can to make sure I come back as strongly and quickly as possible.
"I'm trying to support the team in a different way now, if I can't be on the pitch. That's my situation, and I have to make the best out of it. It's something I'm not used to. I've been quite fortunate, if that's the word, or have done well to avoid injuries in the past, but this is football and I have to get on with it."
Prior to his ankle injury earlier this month, Odegaard had only missed nine games for club and country since joining Arsenal, spending a few weeks out with a hip problem in November 2023 and also taking another blow to the ankle in April 2021, which healed in just over a fortnight.
Odegaard admits he was "scared" by "different" ankle pain
The Scandinavian revealed that the pain of his current issue felt different to when he hurt his ankle three years ago, which "scared" him, although he is grateful that he did not suffer a complete ligament tear.
"I think it was unfortunate to get the injury in the way that I did, but also it could have been worse. It was not a nice twist, and when it happened I felt it could be serious. I've injured my ankle before and the pain felt a bit different this time. That's what scared me, but from what happened it could have been worse, so in that sense I got away with it a bit," Odegaard added.
"Like any player, the first thing I asked the medical team was how long I would be out for, but it's a bit tricky to say at the moment. In the early stages, it's crucial to get a proper rest and to make sure everything heals well. After that it's about getting stronger and building it up again."
Kai Havertz started in the number 10 position in Sunday's 2-2 draw with Manchester City, although the visit of Bolton could offer 17-year-old Ethan Nwaneri the opportunity to make his full debut for the Gunners in the Odegaard role.
Raheem Sterling and Myles Lewis-Skelly are also pushing to start against the Trotters, where 16-year-old Jack Porter could make his debut in goal, as David Raya and Tommy Setford are nursing knocks while Neto is cup-tied.