The Australia selectors have retained the starting XI that did duty in the two-day victory from Perth, while Josh Inglis, Michael Neser and Beau Webster are also included.
Cummins, recovering from a back injury, bowled in training ahead of the Ashes opener and was hoping to play a part in Brisbane which will be a day/night encounter.
The Australia skipper will travel and train with the team and could still be added to the squad for the game that starts on 4 December.
Brendan Doggett, who claimed five wickets in Perth, will likely retain his place alongside pace bowlers Mitchell Starc and Scott Boland if Cummins misses out.
"I am going to control what I can control, keep ticking the legs over, and keep bowling and trying to improve in every session and game," Doggett said on Thursday.
"If I get called on in that second Test, I feel like I am ready to go again."
Usman Khawaja looks set to retain his place in the XI despite not opening the batting in either innings in the first Test due to back spasms.
Khawaja's injury allowed Travis Head to move to the top of the order and score an unbelievable century in the second innings.
Head's hundred has prompted calls for him to be permanent at the top of the order with Inglis and Webster middle-order options.
Australia took control of the second Ashes Test after the third day following a lower-order batting fightback and then taking six England wickets before the close of play.
Australia went to stumps on the second day of the pink ball Ashes Test on 378-6, the home side leading England by 44 runs on the first innings with four wickets still remaining.
Australia Test vice-captain Steve Smith has left the door open to a surprise inclusion of Pat Cummins for the second Test in Brisbane which starts on Thursday.
Australia captain Pat Cummins trained with a pink ball on Tuesday in bid to prove his fitness ahead of the second Ashes Test, which will be a day/night encounter in Brisbane.
