Costa has consistently struggled with his hamstrings in recent months, and the issue flared up again during Spain's international friendly against France earlier this month.
The Brazil-born striker has been in scintillating form since moving to Chelsea from Atletico Madrid in the close-season, with his seven goals in four Premier League outings helping Mourinho's side to a maximum haul of 12 points.
Costa was surprisingly left on the bench for Chelsea's 1-1 UEFA Champions League draw with Schalke in midweek, and Mourinho revealed after that game that the 25-year-old is unable to start several matches in quick succession due to his troublesome hamstring.
However, Mourinho confirmed on Friday that Costa will be unleashed against Premier League champions City on Sunday, as Chelsea look to repeat last season's victory at the Etihad Stadium.
"Everybody is ready to play," the Portuguese said at a news conference on Friday. "Diego is not in the best condition but he will start the game.
"He plays this game so he cannot play against Bolton [in the League Cup]. It's as simple as that.
"We tried to do our best, the player is fantastic in his amazing attitude to be available for the team.
"We have to protect him until he gets completely fit.
"He plays Sunday, he doesn't play against Bolton, he plays against Aston Villa next Saturday. Let's hope he goes in the right direction and is able to play in every game."
