The 25-year-old striker has proved a revelation since moving to Stamford Bridge from Atletico Madrid in the close-season, scoring nine goals in just seven Premier League outings.
However, Costa has been plagued with a hamstring injury that has restricted his ability to train fully, while Mourinho also suggested he was unable to play three games in close proximity.
The Portuguese stated that Costa may benefit from an extended period of rest rather than feature for Spain in matches against Slovakia and Luxembourg this week.
Spain coach Vicente del Bosque did include him in his squad, though, and Costa is adamant that Mourinho never requested he did not feature.
"Mourinho hasn't said anything to me. You have to bear in mind that often I'm the one that makes the decision," he told Marca.
"I have to see how I'm feeling. I have the trust of the gaffer and the coaching staff here. When I have a problem, I say as much. I wouldn't come here and play if I were injured because that would make things worse.
"I've played three matches in the last week. The coach knows the score and that I've had some niggles, which I receive treatment for during the week. I'm hanging in there and am feeling better and better."
Costa also insisted he was not interested in any potential fallout between Mourinho and Del Bosque, saying that his primary focus was on improving for Spain - for whom he has failed to score in five appearances since opting to switch international allegiance from his country of birth Brazil.
"I don't like all that talk [about Mourinho and Del Bosque]," he added. "I've had a lot on my plate with Spain as it is and all I want is to succeed here.
"As of yet things haven't gone as I'd have hoped and as people expected of me. That's only heightened my desire to report for duty and to try to put that right."
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