However, Loic Remy will be available to face the Eagles, having recovered from injury.
Costa has been struggling with a recurrence of a hamstring problem and Mourinho says Chelsea???s results over the last month have allowed him to keep the Spain international on the sidelines.
Asked if Costa would be back on Sunday, Mourinho said: ???It isn???t worth the risk. Over the last month, if we lost a game and we didn???t want to lose a second, he would be back immediately.
???Because the results in the last month were always victories and a draw, we don’t need to rush. Remy is fit, definitely back.???
Asked if Costa may not return to action this season, Mourinho added: ???There is a chance he might not.
???If we win Sunday, I don???t think he will play against Liverpool (the following Sunday). If we don???t win and we need points against Liverpool, I would say he plays. We are on result after result, need after needs.
???He needs a good period. We are preparing a good working situation for him over the summer.???
Three points on Sunday will be enough to clinch the title for Mourinho???s men and he is naturally eager to get the job done as soon as possible.
“It’s easy,??? he said. ???We need two or three points to be champions. Let’s say three, to make sure we don’t depend on goal difference.
“We need a victory or we need three points with three draws. Obviously, we want to finish as soon as possible.
“If we can do it at home, better. If we can do it on Sunday, even better. That’s what we have in our mind.
“Similar to (recent games against) Arsenal and Leicester, we go to win but, at this moment, any point that we get is a positive point.”