Palmer is training again despite recently fracturing his little toe while recovering from a groin injury.
Chelsea boss Enzo Maresca revealed that the England star picked up the knock in a press conference last week.
"He is probably not available for Saturday for sure, Barcelona for sure, or Arsenal for sure.
"Unfortunately, he had an accident at home where he hit his toe. It is nothing important, but he won't be back in the next week. I wake up many times during the night - I hit my head, my legs, my everything - so it can happen."
Cucurella does not believe Palmer
However, this week, Cucurella has admitted that he does not believe the story around the broken toe and blames Palmer’s FIFA skills instead.
"To be fair, I don't believe it. It is true that these things can sometimes happen. I have had this a couple of times, but I'm stronger than them, so I don't feel anything.
“It's a big upset for us because he's getting closer to playing with us, to train with us, and then now he needs to rest. But this is part of life, a part of footballers' lives, we have personal lives, and we have these kinds of problems, so hopefully he can recover fast.
"I don't know. He's running because I think he lost a FIFA game or something like this, I think!"
Palmer has been working with a specially adapted boot that includes additional cushioning to help protect the toe.
The 23-year-old could return next month and still remains a doubt for Sunday’s clash with leaders Arsenal in the Premier League.