Cummins bowled on the outfield ahead of play on the third and fourth days in Adelaide and is due to do so again at the ground on Tuesday.
"Pat continues to improve, bowled with freedom on Saturday and appears likely to play this match although Josh will need more time," national selector George Bailey said. "With that in mind we have retained Michael Neser and Lance Morris in the squad for this match.
"Michael bowled superbly in Adelaide, as did Scott. We were impressed as always with their performances that backed up what they have achieved in the past. Lance is a very exciting prospect who will benefit from time with the squad. With so much cricket ahead, we continue to seek opportunities to grow and maintain our fast-bowling experience and depth."
For Hazlewood there are unfortunate similarities to last season where he picked up a side strain in the opening match of the Ashes and was then ruled out of the series. The hope this time is that he will have the chance to play in Melbourne or Sydney, but the turnaround during the series is very tight.
The performances of Neser and Boland in Adelaide highlighted the pace-bowling depth Australia have on offer.
"Lance Morris has been in the squad, most guys aren't too keen on facing him in the nets. We'll that opportunity at the Gabba on some faster wickets which will be nice. Our stocks are great so keeps things really competitive."
Marcus Harris retains his spot as the reserve batter.
Australia squad David Warner, Usman Khawaja, Marnus Labuschagne, Steven Smith, Travis Head, Cameron Green, Alex Carey, Pat Cummins, Mitchell Starc, Nathan Lyon, Scott Boland, Michael Neser, Marcus Harris, Lance Morris