The Ivory Coast international has been out of action since the opening day of the season after sustaining the damage in the 3-0 loss to Huddersfield Town.
Zaha hinted earlier this month that he could be back on the field prior to the international break, but he has now pencilled in the London derby next month for his return date.
"It's going well, I'm getting stronger," he told talkSPORT. "Hopefully I'll be back soon. I'm trying to be back soon for the Chelsea game. It's hard to watch as obviously I want to help the team going through this hard patch. That's why I'm working so hard at the gym to help the team as soon as possible."
Asked whether he felt Palace chiefs were right to sack Frank de Boer after just 77 days in charge, Zaha added: "I slightly think he should have got a bit more time, as it's not easy to transition from how we used to play to the way we play now. But football is ruthless; if you're not getting the results you get fired."
Zaha enjoyed his best season yet in front of goal last time out, bagging nine assists and seven goals in the Premier League.