But striker Loic Remy is definitely out.
The three all missed Chelsea's 6-0 Champions League club record win over Maribor on Tuesday, but Mourinho said they all have "a little chance" of playing against United, and he would decide after Saturday's training session.
Costa, joint top scorer in the Premier League with nine goals, has missed the last two matches with a hamstring injury and then a virus, while Ramires has missed their last six games with a groin injury and Mikel the last two with a bad foot.
Remy, though, will be out for two to three weeks after injuring his groin scoring the opening goal of the win over Maribor at Stamford Bridge.
Asked if he had any positive news about Chelsea, unbeaten in 12 matches in all competitions this season, Mourinho bounced back: "I only have positive news.
"We are playing well, we are confident, we are top of the league, we are in a good position to qualify for the Champions League, the camp is happy and we are ready for the game."
CLOSE FRIENDSHIP
Matches between United and Chelsea have ranked among the most attractive in the league in recent seasons, and this one is extra special for Mourinho who comes up against his old Barcelona boss Louis van Gaal for the first time in a league match.
Mourinho worked under Van Gaal for three years at Barca, and the two have maintained a close friendship ever since but have only faced each other in one competitive match -- the 2010 Champions League final when Mourinho's Inter Milan beat Van Gaal's Bayern Munich 2-0 in Rome.
Although United are down in sixth place with only three league wins from eight so far, Mourinho says going to Old Trafford is always special -- and that his friendship with Van Gaal will be put on hold for 90 minutes.
"It doesn't matter who the manager is, or the moment, or the league table, or the players, Man Utd is Man Utd and I always look at them through these factors.
"But tomorrow I don't play against Louis, Chelsea plays against Man Utd and during the match I have no time, and he has no time to look around and to see who the opposing manager is.
"Before the match and after the match he is one of my big friends in football so I am always happy to see him.
"Everyone knows the respect I have for him but please on Sunday he is my opponent so don't ask me to speak about him for half an hour now."
(Editing by Ossian Shine)
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