Yorkshire’s first-team coach, who has steered the county to successive Championship titles, was mentioned as a possible bowling coach when the position became available at the end of the summer.
But in a statement on Yorkshire’s website, Gillespie said: “I was made aware that Darren (Lehmann) referred to me by name in a radio interview last month. It appears from media speculation that I am someone that Darren and Cricket Australia wish to speak to.
“At this point in time, I haven’t had a conversation with Darren about any role with Cricket Australia and I have not applied for any role with Cricket Australia.
“I want to make it clear that I am happy in my role with Yorkshire County Cricket Club and Adelaide Strikers.”