Walcott picked up a knee problem during the win over Bolton on Saturday and he missed training on Tuesday.
Koscielny is struggling with an ankle problem, while Ivory Coast star Gervinho is out with a muscle strain.
Arsenal boss Arsene Wenger believes the trio will be fit for the clash with North London rivals Tottenham at White Hart Lane this weekend.
“Koscielny, Gervinho and Walcott are not fit,” said Wenger.
“All three have a chance for the weekend. Walcott could make the derby. He has more than a 50-50 chance.”
