Costa had been struggling with a hamstring problem before he was admitted to hospital with a virus earlier this week to leave him highly doubtful to feature at Old Trafford.
However, at his pre-match press conference, Mourinho has revealed that the Spanish international has a "little chance" of being included in his 18-man squad as Chelsea look to continue their unbeaten record at the top of the Premier League table.
The 51-year-old told reporters: "He has a chance, he has a little chance. The same as John Obi Mikel and Ramires, but the only one that I can confirm that has no chance for Sunday is striker Loic Remy.
"Everything happened to Costa. He was injured and he had go to the hospital with a viral situation that we didn't manage to resolve without being in the hospital over one night.
"It happened before Maribor, but against Maribor he wouldn't have been ready from his injury."
Costa has netted nine goals in as many appearances for the Blues since signing from Atletico Madrid in the summer.