The pace bowler has taken 309 Test scalps in 71 Test matches with an average of 22.10.
The Australian selection chief George Bailey has stated that skipper Cummins will have a crucial role in this winter's Ashes series.
There were concerns that the veteran bowler might sit out due to a ongoing back issue that remained unresolved.
Previous updates from the squad suggested no final decision had been made regarding Cummins' participation, with the Test matches set to start on the 21st of November in the WACA.
Bailey expressed that the captain is progressing and was "optimistic" about the likelihood of taking part.
"It's clear that the window is narrowing and various factors involved, not just the back issue, but additional elements," the selector added.
"We're encouraged. We firmly believe that he's going to play a key capacity. Ideally it's the first Test. If not, then we'll pick it up."
Injury History
Cummins was ruled out the ODI and T20 games against both Asian and Trans-Tasman rivals recently after medical tests showed a lumbar bone stress.
Previous incidents include of recurring issues, with flare-ups in several earlier campaigns leading to absences from multiple domestic campaigns in a short span.
Cummins stated he would be ""aggressive" and "take risks" in his comeback strategy to make the squad for the Ashes.
He mentioned that it was unclear if he had started his bowling workouts as part of his comeback but acknowledged it was "becoming urgent" for him to be fit for the opener.
Alternative Arrangements
Should Cummins not be fit, ex-skipper Smith will take over the captaincy.
Versatile player Green was recently pulled out from the ODI lineup for their limited-overs matches against the subcontinent side as a preventive step because of an abdominal issue.
Bailey described it as a "minor" injury and stated that he'll feature in the domestic first-class competition, so will be "in a good place to deliver overs."
"Considerable effort has gone into creating the schedule for him to be available for the first Test as an batting and bowling option," Bailey explained.
"Originally, he'd only feature in the initial matches in any case. How he handles the willow in shorter formats, if it causes any delay for 24 more hours, we just made the decision to approach this more conservatively."
Match Calendar
The Historic Rivalry
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