The 32 million pounds ($52.22 million) Brazil-born Spain striker, who has scored seven goals in four Premier League games since joining from Atletico Madrid, is struggling with a hamstring injury and played only a bit-part in Wednesday's Champions League draw against Schalke 04 at Stamford Bridge.
"Diego is not in the best condition but he will start the game," Mourinho told reporters on Friday. "He plays this game, he won't play against Bolton (in the League Cup), and he plays against Aston Villa. Let's see his evolution.
"The medical department are doing their best, the player is fantastic in trying to play and being available for the team. We have to try to protect him until he gets completely fit."
Veteran striker Didier Drogba, back at Chelsea for a second spell after scoring 157 in his first, is in no doubt that Costa is now the main man at Stamford Bridge.
"Diego is the striker we needed this season," he said. "When I look at him, I can see the desire to win every challenge, to score goals. He's hungry for goals and that's the best thing for a team like us."
Even with a misfiring forward line last season, Chelsea managed to win at City, although ultimately Mourinho's side stumbled in the title run-in.
After adding the likes of Cesc Fabregas, Filipe Luis and Loic Remy to their ranks during the summer, Chelsea look a perfectly-balanced side this season and with four straight Premier League wins look like being the most serious threat to City's hopes of retaining the title.
Yet Mourinho said the importance of Sunday's clash at The Etihad should not be blown out of proportion.
"It's one more game, three more points," Mourinho said. "Obviously when matches are between title contenders every point makes a difference.
"Last weekend Arsenal and City got one point each, nobody got three. These matches in the end can be important, but if you analyse with a simple pragmatic view it's one game, three points, no more than that.
"For the title it's not just City, there are other teams in this race. Other clubs have exactly the same ambition.
"Last season we had the experience and we know what it is to win there and to lose there. I'm not exhaustively going through every second of these two matches with the players.
"Last season is last season; statistics belong to history, not to the future. What happened last year has no relation to this season. Can we go there and win like we did last season? Obviously we can. But we can also lose."
Victory would be Mourinho's 164th in charge of Chelsea, equalling Dave Sexton's total and leaving him behind only Dave Calderhead on the all-time list.
Points and prizes are all Mourinho craves though.
"Numbers are no more than history. I'm totally focused on three points and the Premier League in 2015, rather than history and a certain number of victories," he said.
(Reporting by Martyn Herman; editing by Toby Davis)
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