Costa’s campaign has been punctuated by hamstring problems and the striker will not be risked against the Eagles, with Chelsea needing three points to win the title.
Loic Remy is back from a calf injury, while Thibaut Courtois could return in goal after a minor hip problem.
Crystal Palace manager Alan Pardew will continue to monitor Marouane Chamakh’s fitness levels after confirming the injured striker still needs more work.
Chamakh, out with hamstring trouble, has been back in training as Pardew prepares his squad for their visit to Chelsea on Sunday.
Fraizer Campbell has also been out with the same injury as Chamakh, alongside Joel Ward (shin), while January signing Lee Chung-yong will be hoping for his first Palace start having last week made his debut as a substitute following a foot fracture.