If approved, the 67-year-old who retired in 2016 would become the first African-American to lead the Pentagon.
He would need a congressional waiver as seven years are required between active duty and becoming military chief.
Mr Biden has been facing calls including from Democratic Asian, Black and Latino caucuses to nominate minorities to senior cabinet posts.
Veteran Pentagon official Michèle Flournoy, who would have been the first woman to hold the position, had also been considered a front-runner – as well as Jeh Johnson, a former Pentagon general counsel and former secretary of homeland security.
Four-star Gen Austin served under the Obama administration, leading the US Central Command, whose area of responsibility includes the Middle East, Central Asia and part of South Asia, between 2013 and 2016. He was the main military architect of the US-led offensive against the Islamic State group in Iraq and Syria.
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.
Gen Austin has a reputation for strong leadership and for avoiding the public eye, giving few interviews and opting to not speak publicly about military operations.
Gen Austin had once been viewed as a long-shot candidate but in recent days emerged as a top-tier contender and a safe choice, Politico reported citing three people familiar with the situation.
But the nomination could draw criticism from some progressive groups over Gen Austin’s position in recent years as a member of the board of directors of defence contractor Raytheon and opposition from lawmakers in Congress who favour a clear civilian control of the Pentagon.
The required congressional waiver has been granted only twice, most recently in the case of James Mattis, the retired Marine general who served as President Donald Trump’s first defence secretary.
Mr Biden and Gen Austin have not commented. The president-elect offered and Gen Austin accepted the post on Sunday, reports said.
News of the nomination emerged ahead of a meeting between Mr Biden, Vice President-elect Kamala Harris and civil rights groups on Tuesday. Rev Al Sharpton, the civil rights activist, said the decision was “a step in the right direction but not the end of the walk”.
The reported decision comes two weeks after Mr Biden announced other senior members of his national security team.
Mr Biden defeated Republican President Trump in the 3 November election. The president continues to refuse to accept defeat in the election, alleging, without evidence, there has been widespread fraud.
Source: BBC
