Gillespie, who has taken 402 wickets for Australia across formats, thinks the five-time World Cup winners might not be the favourites this time but their abundant experience in winning the prestigious tournament will serve them well.
"Every other team in this World Cup knows that Australia know how to win World Cups," Gillespie told ESPNcricinfo. "That is something that will be in every other country's mind, that Australia - while they might not be seen as favourites - they know how to win World Cups.
"So for me, I think Australia are very much a dark horse and I wouldn't write them off, that's for sure."
Every other team in this World Cup knows that Australia know how to win World Cups.
The current Sussex coach opines that home advantage makes England the "favourites" and their recent success in limited-overs cricket make them worthy of carrying the tag. Gillespie also admitted that seeing a England-Australia final at the Lord's would be an "amazing spectacle".
"There's been a lot of talk of England being favourites and playing at home and I certainly think they deserve that tag," he said. "They've played some wonderful 50-over cricket. They've been really innovative and shown a lot of aggression with bat and ball, they've been really dynamic in the field.
"I think it will just be managing the expectations in England. Personally, selfishly, I'd love to see an England - Australia final at Lord's. I think it would be an amazing spectacle," he added.
Australia have been in a terrific form in one-day internationals lately. They came back from a 2-0 deficit against India last month to comprehensively win the five-match ODI series. Captain Aaron Finch, who rediscovered his form in India, then went on to lead the side to a 5-0 whitewash over Pakistan in the United Arab Emirates.
Australia, who lost four ODI series since the start of last year (twice to England and once each to India and South Africa), have peaked at the right time and Gillespie was lavish in his praise for the rejuvenated side.
"They'll take a lot of confidence going into this World Cup," Gillespie said. "Of course I want to see Australia do well. They've copped a lot of stick in recent times but in the last couple of series in India and Pakistan, they've shown some real promise and they've played some really, really good cricket."