Head coach Darren Lehmann has been on the look-out for a replacement since Craig McDermott stepped down at the end of the World Twenty20 in India this year.
He said last month that the highly-regarded Gillespie, who has been head coach at Yorkshire for four years and was last year touted as a candidate for the England coaching job, was high on his list.
At the time, the former Australian fast bowler said he was committed to the reigning English county champions. But the Sydney Morning Herald reported Wednesday that discussions about bringing him home were now at an advanced level and his services could be secured next month.
"We're speaking with a number of candidates but by no means is anything confirmed," a Cricket Australia spokesperson said in response.
The Herald said the pending appointment would propel Gillespie into the frame to eventually replace Lehmann, alongside frontrunner Justin Langer.
Ex-Tasmania quick Adam Griffith is temporarily filling the bowling coaching role for Australia's upcoming one-day tri-series in the West Indies, which also includes South Africa.
Former South African pace spearhead Allan Donald then takes over for their Test tour of Sri Lanka.
Donald has said he is interested in the job full-time with reports also mentioning former Australian pacemen Ryan Harris and Andy Bichel, along with New Zealand's Shane Bond, as possible contenders.