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The Yorkshire coach, who made 71 Test appearances for Australia, has long been linked with a position on the international stage, but continues to reject reports he has spoken with CA.
It had been suggested the 41-year-old might be persuaded to join Darren Lehmann's set-up as a bowling coach.
But Gillespie told Fox Sports: "Just to be absolutely clear, I have not spoken to CA about a role with the Australian cricket team.
"Darren mentioned my name in a radio interview a while back [in April] re: me being involved, so it stands to reason that I will be linked to certain positions.
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"Bear in mind I have not applied for any role with CA nor do I intend to. I am currently very happy in my roles with Yorkshire CCC and the Adelaide Strikers."