The forward has missed the last two games with a groin injury - a problem which has thrown his participation in Roy Hodgson's squad to travel to Brazil into doubt.
With the England manager due to announce the initial party on Monday - the day after the Premier League season concludes - Wenger revealed that Oxlade-Chamberlain is facing a race against time to be fit.
"His time is getting short now but I am still convinced he can do it, if he gets over the next hurdle," he said.
"He has restarted training, so in the next three or four days, we will know more about him.
"His groin is inflamed. I don't believe he'll need surgery - we'll stop him before that. If we see that by pushing him, we could get to surgery, we will stop him completely. We will not take that gamble.
"But if he doesn't get over the next three or four days, then we have to rest him and see. The next three or four days will be vital for him.
"He is desperate to go - who wouldn't be? But we are in a job where your body responds or it doesn't respond. In the end, you need your body to play football."
Arsenal bring their season to a close with a trip to Norwich City on Sunday.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
