Jose Mourinho has bemoaned the absence of the Â£32million signing from Atletico Madrid, who has scored nine goals in seven Premier League games despite a persistent hamstring problem.
The 26-year-old Spain forward missed the matches with Crystal Palace and Maribor and spent a night in hospital earlier this week, but could feature at Old Trafford.
"Diego has a little chance," Mourinho said.
"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."
Costa's recovery from his niggling hamstring problem was delayed by the bout of illness, as he was barred from Chelsea's Surrey training base.
"The problem is that being ill obviously didn't help his recovery process because we didn't want him here at Cobham," Mourinho added.
"The medical staff were going to meet him at his house."
Now Mourinho confirmed he had returned to training on his own.
Loic Remy is out of the Manchester United match after sustaining a groin injury in Chelsea's 6-0 Champions League defeat of Maribor on Tuesday night
Mourinho added: "The only one that I can confirm has no chance is Remy
I would say two weeks, three weeks (out)."
Midfielders John Obi Mikel (foot) and Ramires (groin) could also return alongside Andre Schurrle, who has recovered from illness.
Cesar Azpilicueta is suspended for the first of three matches after his dismissal at Palace, with Filipe Luis likely to replace him.
Thibaut Courtois will return in goal in place of Petr Cech, who started against Maribor.
"I start with Thibaut," Mourinho said.
Source : PA