Mourinho opted to select the Spain striker, who has scored seven times in four Premier League matches this term, only as a substitute in Wednesday night's 1-1 draw with Schalke in Champions League Group G.
The £32million summer signing from Atletico Madrid is not ready to play more than one game a week, according to Mourinho, after a hamstring problem recurred while on international duty earlier this month.
"Everybody's ready to play," Mourinho said.
"Diego is not in the best conditions, but he will start the game
He plays this game, he cannot play against Bolton
It's as simple as that
"I know clearly that we have to try to protect him until he gets completely fit."
The City trip is the first of four key domestic fixtures in Champions League weeks for the Blues, who will hope to swiftly find a solution to Costa's niggle.
The trip to Sporting Lisbon is followed by a home clash with Arsenal, Manchester United away follows the Maribor home tie and a date at Liverpool is immediately after the trip to Slovenia.
"In this moment I don't have this problem," Mourinho said.
"He plays Sunday, doesn't play against Bolton (in the Capital One Cup next Wednesday)
He plays against Aston Villa Saturday (September 27).
"In this moment decision made
Let's see his evolution, let's hope he comes in the right direction and becomes available to play every game."
After 13 years with Chelsea, Frank Lampard is now part of Manchester City's squad, having moved to the Etihad Stadium on loan from New York City FC.
Lampard has made just one appearance for City so far - he was hauled off at half-time at Arsenal - and may not feature against his former club, but Mourinho does not believe it would be odd to see the midfielder line up against Chelsea.
Mourinho said: "No
It's football
I wouldn't imagine that if you ask me one, two, three, four, five years ago (it would be strange).
"Even a few months ago, when he signed for the New York team, I was not expecting that
I thought he was going to New York.
"It's his life, it's his decision."
Source : PA
Source: PA