Saliba was forced off early in Arsenal's defeat at Liverpool last week.
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The defender suffered ankle damage and L'Equipe is now reporting he faces three to four weeks on the sidelines.
It means Saliba could miss Premier League games against Nottingham Forest, Manchester City and Newcastle as well as the start of the Gunners' Champions League campaign away to Athletic Bilbao.
The absence of Saliba opens the door for Cristhian Mosquera, with the summer signing from Valencia impressing at Anfield after replacing the Frenchman a week ago.