For the series opener against West Indies in Barbados, Australia named Josh Inglis to bat at No.4 in place of Steve Smith, who could be back from his finger injury in time for the second Test.
Sam Konstas shifts to the top of the order to replace Labuschagne as expected in an otherwise unchanged XI from that which suffered a shock loss to South Africa in the WTC Final.
In his first Test match at No.3, Green contributed a meagre first-innings score of 4, then a second-ball duck making his Test comeback from a back injury against the Proteas at Lord's.
But despite Green's tough return match, Australia is still keen on playing the allrounder higher up the order than the No.6 where he has typically featured at Test level.
"We see that (No.3) as a long-term option," Cummins said.
"Going in to last week, he's hitting the ball really well. He's moving really well. He had a Test match where it obviously didn't go to plan.
"The message is not to look too much into that. We're really happy with where his game is placed. I dare say he'll get a decent run at No.3."
It looms as a setback for Labuschagne, who had been a mainstay for Australia at No.3 until his axing from the set-up following one Test opening the batting in the WTC Final.
Labuschagne has averaged 27.82 with the bat for the past 12 months, well down on the 62.3 he managed across the four calendar years between 2019 and 2022.
With a glut of batting talent available, and Australia vowing to give Green their patience, Labuschagne's path back appears clouded ahead of this summer's home Ashes.
"If there's an opening, we could see him kind of fighting his way back into the Test team at some point, but obviously the focus now is giving a couple of other guys a go," Cummins said.
"He's had a pretty good run and obviously didn't make the most of it as well as he would have liked, so (we're) offering that opportunity to the next couple of guys."
Australia's batting headaches could resume as soon as next week as Smith fights to return from the dislocated finger he suffered in the WTC Final loss earlier this month.
The Test vice-captain is recovering at his New York holiday home and would likely bump Inglis from the XI should he be fit for the second Test in Grenada.
"Hoping so (Smith will be available)," Cummins said.
"I know the medical team have got a bit of a program for him, so no huge update. Hoping it goes well and he'll be back here towards the end of the match, but he's got a few things to tick off."
AUSTRALIA TEAM: Sam Konstas, Usman Khawaja, Cameron Green, Josh Inglis, Travis Head, Beau Webster, Alex Carey, Pat Cummins (c), Mitchell Starc, Nathan Lyon, Josh Hazlewood
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