The Spain international has scored seven goals in his first four games in England's top flight, but the hamstring issues that dogged the back-end of his campaign with Atletico Madrid last season have resurfaced.
Costa defied fears over his fitness to score a fine hat-trick in last weekend's 4-2 win over Swansea City at Stamford Bridge, but he was limited to a late cameo as Chelsea stumbled to a 1-1 draw with Schalke in their UEFA Champions League opener on Wednesday.
Jose Mourinho has a full squad to choose from and, though conceding Costa is not yet ready to play a full schedule, confirmed the striker will line up on Sunday at the Etihad Stadium - where Chelsea won 1-0 in the league last term.
The manager said: "Diego is not in the best condition but he will start the game.
"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 [Wanderers on Wednesday in the League Cup], he plays against Aston Villa next Saturday, let's hope he goes in the right direction and is able to play in every game."
Mourinho's counterpart Manuel Pellegrini will be desperate for a win as City are the closest of Chelsea's predicted title challengers, but already sit five points off the pace.
A reaction is also required from the champions in their third big game in the space of nine days.
Martin Demichelis rescued a 2-2 draw at Arsenal last Saturday before Jerome Boateng came back to haunt his former club, striking late to secure a 1-0 defeat for City at Bayern Munich in midweek.
Pellegrini was also shorn of his star striker for large parts in Germany, with Sergio Aguero only fit enough for a 16-minute showing from the bench.
But the Argentina star is also set to start on Sunday, much to Pellegrini's relief, having suffered defeat to Chelsea in each of last season's Premier League meetings.
The Chilean explained: "He's fresh for Sunday and I am sure that we will make a difference.
"When he is 100 per cent fit he makes a difference."
Aguero's return is a boost to Pellegrini but the 61-year-old is without the injured Stevan Jovetic (hamstring) and Fernando (groin).
