The Gunners boss revealed on Monday that the Polish international picked up a rib injury in the North London side's 3-1 win over Norwich on Saturday.
"Fabianski is a major doubt, but we will decide that tomorrow [Tuesday]. He got a kick in the rib [against Norwich City]," Wenger told Arsenal's official website.
If Fabianski is unable to play, Wenger may be forced to reinstate fellow Polish goalkeeper Wojciech Szczesny, who has been recently relegated to the bench in favour of Fabianski after losing his form recently, something that the Arsenal boss has described as a "blip."
Meanwhile, Tomas Rosicky is able to return to the squad after successfully recovering from a hamstring injury that saw him sit out Arsenal's win against Norwich. The Czech international scored both goals in his side's 2-0 victory away to West Brom when he was last in action.
Per Mertesacker is also available for selection after returning from suspension. The German center back picked up a one-match ban when he was shown a straight red card in the clash against the Baggies.