The Gunners centre-back has been out of action since rupturing his Achilles against Atletico Madrid in May, costing him his place in France's victorious World Cup squad.
Koscielny, 33, is way ahead of schedule, and could now make his first appearance of the season sooner than expected.
It was reported that the ex-Lorient defender would have to wait until December to get his first minutes of game time.
But the Arsenal skipper is determined to get out over the next month in what would be a huge boost to the North London clubs push for the top four.
Boss Unai Emery revealed on Friday that he would not be rushed back into the first-team quickly.
He said: "We need to be calm with him. Calm because we need [to wait] more than a month.
“He needs to feel [well] first, if he is doing some things, then he is doing well."
While also adding: "I think we need also to give confidence to him, to be close with us because it was a big injury.
“But now he is getting better, he is training with us in some things and this is very positive."
Arsenal welcome Leicester to the Emirates tonight, with Emery looking to rack up his tenth successive victory in all competitions.
A win for the home side would see them leapfrog rivals Tottenham into fourth spot, while also going on level points with Chelsea in third.
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