The Premier League's top goalscorer has missed his side's last two games with ongoing hamstring trouble but was also struck down by illness before the midweek Champions League win over Maribor.
The virus was serious enough for Costa to spend a night in hospital, and he is yet to train with his team-mates ahead of the Super Sunday trip to Old Trafford.
But Jose Mourinho said: "Diego has a little chance. I'm not saying he can play. I'm saying that we are trying. We will see what happens between Friday, Saturday and Sunday.
"Everything happened to him. He was obviously injured and he had to go to the hospital with a viral situation that we didn't manage to resolve without being in hospital over one night.
"The problem is that being ill obviously didn't help his recovery process because we didn't want him here at Cobham. The medical staff was going to meet him at his house."
Costa's absence would leave Didier Drogba as Mourinho's only recognised centre-forward available as Loic Remy remains out.
The France international has a groin problem, and the Chelsea boss estimates his rehabilitation period at "two weeks, three weeks".
Mourinho also confirmed Thibaut Courtois will start in goal in Manchester, while John Obi Mikel, Ramires and Andre Schurrle all have a chance of playing after injuries and illness.