Costa was in hospital earlier in the week with a viral infection and hasn't played since returning from international duty as he has been struggling with a hamstring injury.
Mourinho confirmed that striker Loic Remy will miss the trip to Old Trafford after injuring his groin whilst scoring in the 6-0 win over Maribor in the Champions League in midweek, and expects the Frenchman to be ruled out for up to three weeks.
Speaking at his pre-match conference, Mourinho said on Costa: "Everything happened to him. He was obviously injured and he had to go to hospital with a viral situation that we didn't manage to resolve without being in the hospital over one night.
"The problem is him being ill didn't help his recovery process because he wasn't here [at the training ground]"
Costa has trained on his own this week in order to get himself fit, and the Chelsea boss said he didn't know if Didier Drogba will start the game for Chelsea at Old Trafford but seemed to know he could rely on his more experienced forward.
"His contribution to this team will always be important... The moment Diego couldn't play and especially now that Remy can't play, he understands the responsibility, he understands the needs and he pushes himself to different levels for the team."
Thibaut Courtois will start in goal after Petr Cech was given the nod for the Champions League win over Maribor but Ramires and John Obi Mikel are unlikely to play any part.
After last season's 0-0 draw in the same fixture between the sides, Mourinho has said his side will go to Old Trafford with the intention of winning the game, and seems to be treating Louis van Gaal's side with the utmost respect, regardless of their league position.
Mourinho added: "We are confident, in a good moment, a good situation and there is no reason for us to change our feeling.
"Man United is Man United. For me, it doesnt matter the manager, the moment, the table, it doesn't matter [who] the players [are]. Man United is Man United."
This is first time that Juan Mata will face his old club after departing Chelsea last season, and Mourinho still speaks highly of the man who left for £37 million.
"For me Juan is a very good player and I look at him as a very good player, and I don't look at him as a special player because of certain circumstances."