The striker returned from international duty with Spain this week and has been undergoing treatment on the problem.
Mourinho also revealed that Ramires, Didier Drogba, Andre Schurrle and John Obi Mikel were also doubts for this weekend’s game.
Asked if Chelsea have any injury problems ahead of Saturday’s trip to Selhurst Park, Mourinho replied: “A few, but I want to wait until tomorrow.
“We have some problems, yes. Ramires, Drogba, Diego Costa, Schurrle, Mikel, it’s a long list.”
Mourinho confirmed that Costa returned to Cobham early this week to undergo treatment.
He added: “The Spanish team played in Luxembourg on Sunday. I gave them Diego, [Cesc] Fabregas and [Cesar] Azpilicueta.
“I gave them two days off, Monday and Tuesday, so they had to report to train on Wednesday at 3pm. And Diego was here Monday at 9am. So you can imagine how strong he was to be here at 9am on Monday.”
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