Steve Smith will captain the side in his absence.
Australia head coach Andrew McDonald is due to address the media at 12:15pm AEDT on Monday to discuss Cummins' rehabilitation.
McDonald had previously said that Cummins will need to be bowling for "at least four weeks" to return to full match fitness, a timeline which has now lapsed.
Cummins said via a press release statement that he "expects to return to bowling shortly", following some successful running drills at Cricket Central in Sydney last week.
The second Test in Brisbane is five and a half weeks away (December 4), which in itself could be a race against time.
Monday morning's confirmation from Cricket Australia will allow Cummins to focus on his recovery from a lumbar stress injury without any speculation about his availability for the opening game of The Ashes, whilst it is almost certain that 36-year-old Scott Boland can now spend the next three and a half weeks getting ready for his 15th Test appearance and his first in Perth, with Optus Stadium the only of Australia's six major Test venues that he has not yet appeared at in this format.
The news will also intensify the attention on Tuesday's third round of Sheffield Shield matches in Melbourne, Brisbane and Perth, which will act as a further audition for next week's first Test squad, which will need one backup fast bowler.
Leading candidates include Sean Abbott and Michael Neser, whilst outsider Fergus O'Neill can make a further claim after a first innings 5-26 against New South Wales last week.
New Test all-rounder Beau Webster has also returned to bowling in a bid to keep his place at number six, which would require Marnus Labuschagne to accompany Usman Khawaja at the top of the order in his near-certain recall.