The Brazil-born Spain international hit the ground running after signing from Atletico Madrid in the summer, scoring seven goals in his first four Blues appearances.
But he has netted only twice in his last seven, having been hampered by hamstring problems, and has been overtaken as the Barclays Premier League's leading scorer by Sergio Aguero of Manchester City.
Mourinho's men suffered their first defeat of the season at Newcastle on Saturday, with Costa again failing to trouble the scorers.
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But Mourinho told several national newspapers: "For me, the problem is not the goals - they will come as a consequence of his condition.
"He has to improve his condition. He was injured and had many doubts because he went a long time without training.
"Obviously that must have an effect on a player in the way he runs, the way he moves and in his co-ordination.
"I don't think there is any problem but he has to recover."
It remains to be seen whether Costa will be given the chance to build his match-sharpness in Wednesday's Champions League clash with Sporting Lisbon, with Chelsea having already qualified for the knock-out stages.
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