The Gunners travel to Stamford Bridge, knowing that victory will take them nine points of their London rivals.
Cole suffered a back strain in England's midweek draw with Portugal and Wenger confirmed he would not be involved - but he could still play against Celta Vigo next week.
"Ashley has a stiff back," said Wenger. "He came in and it was very stiff and very inflamed.
"We believe he will be short for Saturday's game but he might have a chance to play on Tuesday."
Midfielder Gilberto Silva is also a doubt after being stretched off playing for Brazil against Ireland, while Ray Parlour is definitely out.
"Gilberto has a bad knock on his ankle but fortunately it is not twisted. We will see how he responds to treatment today and training tomorrow. There is small possibility for Saturday," he added.
"But Ray Parlour (knee) is out as well so our options are shorter now. It is important not to get anymore injuries."
On the positive side, Wenger added that Thierry Henry and Sol Campbell will be fit - while Freddie Ljungberg could also feature.
"Thierry should be okay," he added. "We pulled Sol out [of the England squad] with a groin problem. We did not want to overload him with games. He is carrying on with that problem but he should be able to play on Saturday.
"Freddie could be available," he said. "But he only joined up with the rest of the squad today. So we'll see what I do about him."
