After missing the T20 series against England due to a foot injury, Healy is desperate to be part of the first women's Test at the MCG since 1949.
The 34-year-old will take part in Australia's session under lights on Tuesday to give herself a chance of featuring in the four-day match, starting on Thursday.
"She's going as well as can be expected," Australia coach Shelley Nitschke said, having already secured a series win in the multi-format Ashes.
"You've all seen her out in a boot and taking some weight off that foot.
"She will have a test (on Tuesday), and we'll just sort of see where that lands and have some discussions about that, whether or not we think she's going to be OK for a four-day Test."
Alyssa Healy was all smiles during the T20 series despite her foot injury. (Mark Evans/AAP PHOTOS)
If Healy does play it will be as a batter only, with Beth Mooney to retain the gloves after a successful stint behind the stumps in the T20 games.
Healy's injury could open the door for rising star Georgia Voll to make her Test debut after impressing early in her international white-ball career.
But allrounder Ashleigh Gardner seems certain to return after also missing the resounding T20 thumping.
The reigning Belinda Clark medallist spun Australia to victory in the last Test against England back in 2023 in Nottingham.
"She's tracking really well," Nitschke said of Gardner.
"I expect her to track fully and be available for selection."
Australia swept England 3-0 in both the ODI and T20 series, taking an unassailable 12-0 points lead.
If Australia win the Test, they will complete the first whitewash since the multi-format Ashes series was introduced back in 2013.
Nitschke insisted the clean-sweep hadn't been spoken about "a lot" but admitted it would be another great achievement for her all-conquering team.
"A clean sweep would be amazing … hopefully we can get into a position to make that possible but I don't think we'll get too far ahead of ourselves," she said.
Nitschke stayed clear of responding to England coach Jon Lewis's recent claims Australia had an advantage in athleticism due to the "cultural difference" and the warmer weather down under.
England star Nat Sciver-Brunt believed her team had regrouped following a horror collapse in Adelaide to end the T20 series.
"The last few days have been tough, there's no two ways about that ... but this being a Test match at the end of that ... hopefully we can put a good showing of ourselves," she said.
Despite staring at a historic thrashing, Sciver-Brunt insisted the previous tour of Australia in 2021-22 was harder due to the restrictions that were in place because of the COVID-19 pandemic.
"It's been tough," the gun batter said
"Coming in with probably a bit higher expectations than before and we just haven't really given the best showing of ourselves."
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