There is also hope that both Gabriel Magalhaes and Jurrien Timber, who limped off during Sunday’s draw against Liverpool, will not be long-term absentees.
But the key midfielder is taking a significant step towards fitness, with the 25-year-old scheduled to return to training on the grass this week.
There is doubt over when Arteta will deem Odegaard to be fit for selection, however.
Martin Odegaard is accelerating his recovery from an ankle injury to deliver a timely fitness boost to Arsenal
If Odegaard plays before the next international break - which commences after the away clash at Chelsea on November 10 - then Norway will be within their rights to call up the former Real Madrid star for their matches against Slovenia and Kazakhstan.
Indeed, Norway manager Stale Solbakken said this week that he ‘hopes’ Odegaard is ready to be available for the their November fixtures.
There will be apprehension at Arsenal about Odegaard reporting for international duty so soon after his return to match fitness.
But with tough fixtures against Newcastle, Inter Milan and Chelsea on the horizon, Odegaard’s availability would certainly arrive as a major boost ahead of a difficult run of fixtures.
Elsewhere, Magalhaes is being assessed after a taking a knock to the knee in the 2-2 draw versus Liverpool.
Early indications are that the Brazil international will not be a long-term casualty but will have a definitive scan on Tuesday to confirm the extent of the injury.
Meanwhile, Timber complained of calf tightness after the game amid hope the Dutchman may have been suffering a bout of cramp given the game against Arne Slot’s team was the defender’s first outing in just under a month due to muscular problem.
Arsenal are yet to confirm the extent of the knee injury suffered by Ricardo Calafiori in last week’s win over Shakthar Donetsk, though it is understood he will miss weeks rather months.