The Spain international has been nursing a hamstring problem in recent weeks which kept the 26-year-old sidelined for most of April after he suffered the blow against Stoke City.
Mourinho had earlier hinted that Costa could return against Arsenal or Crystal Palace, but the Blues boss relied on veteran striker Diego Costa and the returning Loic Remy.
Speaking at his pre-match media conference at Cobham training ground on Friday afternoon, Mourinho gave an update on the Chelsea striker’s fitness status.
“Diego Costa wants to play but I will protect him all the way. We need to find a balance between the risk and the desire,” Mourinho said.
Mourinho added that Brazil international Oscar is injured with a thigh problem and won’t feature for his country at Copa America.
Jose: 'Oscar has a thigh injury. We spoke with Dunga and he made the decision it was impossible for him to go to the Copa America.' #CFC
— Chelsea FC (@ChelseaFC) May 8, 2015
Chelsea were crowned Premier League champions last weekend after a 1-0 victory over Crystal Palace at Stamford Bridge.
Mourinho has guided the west London side to three titles during two spells at the club.
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