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.
Mr Biden’s reported decision comes two weeks after he announced other senior members of his national security team.
Mr Biden and Gen Austin have so far made no public comments on the issue.
Earlier media reports suggested that the Democratic president-elect would nominate veteran Pentagon official Michèle Flournoy for the job. She would have been the first woman to hold the position.
Mr Biden defeated Republican President Donald Trump in the 3 November election, and is due to be inaugurated on 20 January.
Mr Trump continues to refuse to accept defeat in the election, alleging, without evidence, there has been widespread fraud.
Who is Gen Austin?
Politico first reported about Mr Biden’s decision to appoint Gen Austin as defence secretary, citing three people familiar with the situation.
It said Gen Austin had once been viewed as a long-shot candidate – but that in recent days he had emerged as a top-tier contender and a safe choice.
CBS, the BBC’s US media partner, later quoted multiple people familiar with the plans.
It said Gen Austin’s emergence as a potential choice came amid growing calls from national civil rights organisations and Democratic Asian, Black and Latino caucuses to ensure that Mr Biden nominated minorities and women to senior cabinet posts.
Joe Biden (left) and Gen Lloyd Austin in Iraq in 2011.
The four-star general in 2013-16 led the US Central Command, whose area of responsibility includes the Middle East, Central Asia and part of South Asia.
Before that he was vice-chief of staff of the army and the last commanding general of the US forces in Iraq.
During these years he worked closely with Mr Biden, who was vice-president in the Barack Obama administration.
But Gen Austin faces a couple of hurdles, including his position in recent years as a member of the board of directors of defence contractor Raytheon, according to CBS.