The series opener is scheduled to start at the Adelaide Oval on Dec. 17 but a new cluster of coronavirus cases in the state has cast doubts on whether the match will ahead as neighbouring states closed their borders with South Australia.
Hazlewood said if they were to play at the Gabba, the fast bowlers would rather get the game out of the way before it became hotter and favoured the batsmen.
"It probably would be (the Gabba) to be fair," Hazlewood told reporters.
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"I think the longer we wait the hotter it gets up there so the quicks would all be happy to get that game done in early December. We obviously have a really good record (in Brisbane) and it's a great place to start."
Australia have not lost a test match at the Gabba since 1988.
The outbreak in Adelaide forced players such as captain Tim Paine into self-isolation while others preparing for the domestic Big Bash League were moved to a training camp on the New South Wales coast.
Cricket Australia, who had hoped to fill the Adelaide Oval with 27,000 fans - half its capacity - said on Tuesday that they "remained committed" to playing the day-night test match at the venue and were monitoring the situation.
Australia will first face India in three one-day internationals and three Twenty20 matches starting Nov. 27 in Sydney. (Reporting by Rohith Nair in Bengaluru; Editing by Toby Chopra)
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