Gen Austin, aged 67, will become the first African-American to lead the Pentagon.
Gen Austin, who led US Central Command during the Obama administration, would need a congressional waiver as it is less than seven years since he retired.
Biden’s reported decision comes two weeks after he announced other senior members of his national security team.
Biden defeated Republican President Donald Trump in the 3 November election, and is due to be inaugurated on 20 January.
Trump continues to refuse to accept defeat in the election, alleging, without evidence, there has been widespread fraud.
(With inputs from Agencies)
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