Australia and New Zealand will meet again in the Second Test from December 26 at the MCG, with Hazlewood unavailable due to the hamstring injury he sustained in Perth.
James Pattinson looms as the favourite to step in, while Michael Neser and Peter Siddle are in the mix.
Australia wrapped up the First Test inside four days, ensuring their bowlers earned an extra days’ rest ahead of Boxing Day.
“We certainly weren’t going to bowl them into the ground,” Australia captain Tim Paine said, about quicks Mitchell Starc and Patrick Cummins.
“We thought we could still get the job done with those conditions in our favour with Nathan (Lyon) in our side and not have to flog them to death, because they are obviously hugely valuable for the rest of this series and in all three formats for Australia.
“We wanted to make sure we managed them correctly and didn’t ruin their series.
“When you’ve got Lyon in your side it makes it a hell of a lot easier.”
The MCG pitch is an added factor for both sides, with the deck proving batsman friendly in recent years.
Coach Justin Langer wouldn’t be drawn on the likely make-up of his XI for the Second Test.
“If the wicket is like it’s been the last few years we might even be able to play four quicks and a spinner,” Langer said. “There’s lots of combinations.”
Langer had said on Sunday: “The obvious one would be Peter Siddle actually. He did a really good job for us in the Ashes and he is bowling really well for Victoria.
“The Test is at the MCG where he has played a lot of cricket. We will see what happens for the rest of this game and then make a decision.”
Langer didn’t rule Hazlewood out of playing in the Third Test in Sydney from January 3.