The 41-year-old, known universally as "Dizzy", was mentioned as a target to join the Australia staff by head coach Darren "Boof" Lehmann after McDermott stepped down the wake of the World Twenty20 earlier this year.
Gillespie, however, said he had no intention of abandoning his job at English county Yorkshire, who he has led to successive County Championship titles, and heading back Down Under.
"Darren had mentioned on radio in Australia that he'd be keen to get me back into the system over there," he told the BBC.
"I was always going to catch up with Darren when he was over here because he's one of my best mates, but I got stuck into him a bit because he didn't need to mention my name on the radio.
"I informed him I wouldn't be applying for a role so we can end the speculation. I was not offered a job and I have made it very clear that I would not be applying for any role with Cricket Australia."
Former South African quick Allan Donald will mentor Australia's bowlers for the upcoming test series in Sri Lanka, while West Australia's Adam Griffith is in charge for the limited overs series against West Indies and South Africa that precedes it.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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