Koscielny missed Arsenal’s last Premier League outing against Brighton over two weeks ago due to an ongoing Achilles tendon injury.
The France defender also missed out on his nation’s two World Cup qualifiers over the international break.
But Arsenal have hope of having the 32-year-old centre-half back in action this weekend against Watford, according to The Telegraph.
The news will come as a huge boost for manager Arsene Wenger, who saw centre-half Shkodran Mustafi pick up a thigh injury while on international duty with Germany.
The Telegraph add that Mustafi, who has started all-but two league games this term, is facing a lengthy spell on the sidelines.
There were also concerns about summer signing Sead Kolasinac, who was forced off at half-time for Bosnia on Tuesday night.
But Kolasinac’s problem was nothing severe and is expected to continue at left wing-back at Vicarage Road on Saturday.
Wenger will have Mesut Ozil and Danny Welbeck back in contention against Watford, with the duo having resumed full training following respective knee and groin injuries.
The Arsenal boss, whose side are undefeated in their last seven outings, will have to make a decision whether to start star man Alexis Sanchez.
Sanchez played late on Tuesday night as Chile missed out on qualification for the World Cup, which could see Theo Walcott recalled to the starting XI.
