Australia will begin their defence of the Ashes in a one-dayer at North Sydney on Sunday, as part of a congested three-week series.
Since the introduction of the multi-format concept in 2013, the Ashes have included three ODI, three T20s a Test with the winner determined on overall points.
But players want more Test match cricket, with the longer-format games growing in popularity and skill.
Not since 2006 has more than one Test been played in a women's series, while the last series to involve three Tests was way back in the 1998 Ashes.
But Gardner said the ideal structure for a multi-format series would include three Tests to go with three T20s and three ODIs.
Players from both England and Australia would like to play more Tests in the Ashes series. (Joel Carrett/AAP PHOTOS)
"It is obviously going to make the tours a lot longer, I am not sure where you are going to fit it in, knowing we have to play overseas as well," Gardner said.
"But personally I would love to see three, three and three.
"I would just love to play more Test cricket against England. Playing the one Test feels like a bit of a novelty at times.
"We have good white-ball games against England and other teams around the world, but the way our teams match up. it would be a really cool Test series."
Gardner took 8-66 in the final innings of the most recent Ashes Test at Trent Bridge in 2023, where the match attracted a world-record crowd of 23,207 across five days.
Cricket Australia are hoping for a sizeable crowd for the day-night MCG Test in this summer's Ashes, from January 30, while England players also want a longer series.
"I completely agree with Ash. I would love to see three, three and three," opener Tammy Beaumont, who scored 208 at Trent Bridge, said.
"The best thing about the Ashes is the narrative, the rivalry and how it builds over time.
"You saw in the India-Australia men's series that the narratives build over a five-Test series and even in a three-match series.
"Things like (Jasprit) Bumrah always getting the same people out.
"As an opening batter that's why you love the game, it's a battle of trying to get one up over an opening bowler. It builds even more in Test cricket."
The calls are, however, unlikely to prompt change.
The ICC's Future Tour Programme for the next four years shows no multi-Test series, while the move of India's WPL to January has caused more of a squeeze.
As such, this series will mark the last time elite women's cricket is played in Australia during the school holiday window until at least 2029 .
"Space in the calendar is a real challenge," Cricket Australia CEO Nick Hockley said.
"What I would like to see is more countries playing multi-format series more regularly."
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