Costa, who scored 20 league goals last season, missed the 1-0 Community Shield defeat by Arsenal at Wembley Stadium last weekend and sat out the club's final pre-season friendly at home to Fiorentina on Wednesday.
Mourinho was cautious when asked if the Brazil-born Spain international would be fit to face Swansea.
"I think he's going to train with the team (on Friday)," Mourinho told reporters. "His reaction after that and his decision to be confident to play is another story.
"I have (Loic) Remy and (Radamel) Falcao. We have bought Falcao because we know we need three strikers. Three is the perfect number and we have three."
Costa joined Chelsea from Atletico Madrid for 32 million pounds last season but the striker missed large parts of the campaign with a persistent hamstring problem.
Mourinho rejected the notion that the champions might need to buy another forward after one reporter joked that Costa's injuries mean the Portuguese coach had 2-1/2 strikers.
"The half, when he plays, is one and a half, so it compensates, because he's a fantastic player," he said.
"I prefer a situation where a player is never injured, never has problems, has 10 months of competition obviously.
"There is nobody to blame. The player (Costa) works hard, harder than before."
One area he is looking to strengthen is left back after Filipe Luis was sold to Atletico Madrid and Mourinho expects to sign a player to compete with Cesar Azpilicueta.
Chelsea romped to the title last season, but master of mischief Mourinho played down expectations when asked what would constitute a good campaign at Stamford Bridge.
"I don't know," he said. "A bad season is you don't perform. If in October you are 15 points behind the leader. If you lose the cups and arrive in March with nothing.
"Let's try to be a good team and be here in March-April speaking about winning something."
(Reporting by Michael Hann; Editing by Ken Ferris)
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