Odegaard has been out since the last international break when he suffered the injury with Norway.
In Saturday's Arsenal match programme, Odegaard said: "In the last week or so I’ve made really good progress.
"I’m getting better and better by the day and feel it’s going well.
"When you feel like things are moving forward, it gives you motivation to do more and more and work harder.
"Today is our last game before another international break, so that gives me some more time to work on the rehab, too.
"Hopefully it won’t be much longer — I think we will know more as soon as I get out on the training pitches and we see how my ankle responds to that.
"At the moment it’s progressing well and it looks better than we were thinking, but we’ve still got to take every day as it comes."
